Thanks for all the great entries! I was really tired when I wrote this so please shout at me if I said anything stupid or messed something up!
Meager Meal (herw)
A change for Ruins was unexpected! I'm not sure whether herw's intention was for this to replace Ruins or be used in addition to the 5 old Ruins or to replace one particular Ruin though. I am of the opinion that Ruins play too similarly to Curses so they don't really open up as much new design space as an alternate junk card could have done, the idea of a self trashing junk card seems like a promising alternative to me.
Vintage (King Leon)
Harvest is an obvious choice for replacement being one of the worst cards in the game for its cost. This is very similar to Harvest and I'm not sure that at $6 is much better than Harvest was for $5.
Blackmail (Chappy7)
Cultist is another super obvious candidate for removal, although for the opposite reason of Harvest. This has a similar feel as Cultist being a junker that you can potentially chain but is much less powerful. I think the problem though is that Witch is a really powerful $5 and changing the Cursing to Ruining is not that much of a downgrade so I'm fairly sure that this card is also incredibly powerful. Having said that this card is much less obnoxious than Cultist and might actually be more fun to play than Witch as after the dust settles having a deck filled with Ruins and Labs seems like a better experience than one with Moats and Curses.
Privateer (faust)
Pirate Ship should get the axe in a 2nd edition for sure. This seems like some kind of combination of Bishop and Pirate Ship. But if you play this for the Islanding then it also powers up your opponents Privateers for money making as well as giving them some free thinning, it seems really weak to me. Miser isn't held in particularly high regard and this seems to be worse than it in almost every way, the only real advantage is that this can remove Estates from your deck. It also has issues when you can't play many Actions.
Digger (NoMoreFun)
I think both Pearl Diver and Lookout are good options to remove. I appreciate that this is trying to get the feeling of 2 cards in one, I like that if you have 2 then the first one can put a bad card on the bottom for the other.
Thimberlig (Asper)
Fool might be my least favourite card in the game, although I quite enjoy Lucky Coin. I didn't like the first version of this because it used Boons and I think it's really bad that 3 out of the 7 Heirloom cards use Boons so I'm glad that Asper changed that. I guess the worry is that Lucky Coin gives a really big boost to money strategies and this card might make a boring money deck too good too often in conjunction with the Lucky Coin. I can't really know whether that is actually a problem without playing with card though.
Skiff (Aquila)
I like the top part of this as a Peddler type thing, not strictly better or worse than Peddler. I suppose it would be nice to have a reaction in Seaside, although Lighthouse is Reaction-like and I feel like Seaside might have no Reactions to balance out Hinterlands having so many? Or maybe I made that up? Anyway, I'm not a huge fan of putting random Reactions on otherwise cool cards and Donald X. seems to regret a few reactions like Fools Gold and Trader so I'm not totally sold on that part.
Farmer (Gubump)
I quite like this, it captures the unique thing that Harvest does but isn't completely terrible. Cornucopia also doesn't actually have a real terminal draw card either so it fills a bit of a gap in the expansion. Hard to tell whether 6 is the correct number without playing any games with it but i think a drawing harvest is a nice idea.
Renovate (mail-mi)
Rebuild is obviously a strongly disliked card so a good choice. As others have pointed out this seems like quite a powerful card, probably in league with Sentry and Junk Dealer and Recruiter and such. It doesn't do too well with Coppers though (unless there's any good $2s of course) and I like that it could impose some interesting decision making if you reveal 2 Coppers and a good card, as you don't really want to trash the Coppers or put them into your hand. A "turbo Renovate) strategy could prove problematic though, as look 3 cards deep should make them fairly easy to chain.
Goldsmiths (ClouduHieh)
I don't know why Mint needs replacing, it's a really cool card! It has a pretty unique dynamic which I really enjoy. This card is basically just a buffed Mint for $6, which isn't particularly interesting to me. Coffers in Prosperity isn't out of the question as Prosperity comes with Coin tokens for Trade Routes and mats for VP tokens (my old version did, I'm not sure whether more recent printings still do), although i don't think prosperity should have Coffers.
Pirate Raid (Shard of Honour)
This card seems very similar to Thief, but you can get the Treasures in hand next turn. It doesn't fix the Copper trashing prolem of Pirate Ship or the scaling issues with more players that Thief had so I can't say I'm a fan of this.
Shipwreck (d)
This doesn't really fit the brief as Seaside doesn't have Projects or Trashing tokens so it wouldn't work in a 2nd edition Seaside set.
Distillery (Commodore Chuckles)
I'd be sad to see the Duchess' baby removed from the game but Duchess is pretty awful. I like that this gives you a reason to want Duchy in your deck as it costs $5 so is nice to reveal with a distillery. I wonder whether this is actually bonkers though, with decent trashing it probably isn't too hard to make this hit a $5 pretty consistently. I think I'd also prefer it if the gain was mandatory as then it would be a bit riskier to balance it out a bit.
Campaign (4est)
I feel like Annex gets more hate then it deserves to be honest. The free Duchy aspect spices up the endgame a bit and it isn't too uncommon that you don't want Province for $8 anyway due to endgame positioning. I appreciate that there isn't a Scheme Event so that's a nice effect you found and I never remember exactly what Annex does either which isn't a good sign for the card really.
Cattle Traders (hypercube)
I think Trader is a decent choice, mainly due to the reaction confusion. I like the discard 2 cards and trash from the discard part. Having the +Buy on here is a bit different I suppose, this is bad when you're finished trashing but not completely useless and could still be instrumental if there's no other +Buy. I think that's pretty funny too. I'm not sure about the reaction, +1 Card is a generically beneficial thing to get but +1 Action is more situational as you actually need an Action to use it, so that doesn't strike me as the best choice for a reaction effect. There is one massive problem with this though and that's that cattle simply don't exist in Dominion (Silk Road is inconclusive) so this card needs a major thematic overhaul.
Inquest (Fragasnap)
Proposing an improvement to Renaissance so soon is a ballsy move. I actually agree about the 2 Durations in Renaissance seeming off for an expansion that's trying to focus on simplicity. I think the Artifact overcomplicates this though and it seems really risky if you let your opponent steal it after you put some tokens on it. I think the way I'd do this is to have the Inquest put tokens on itself to track what it's drawing, then you can even do the fun Apprentice-like decks that Research doesn't do.
Ransacker (MattLee)
This is always going to make at least $1 so it's kind of like Amulet but you get 2 out of the 3 options. It'll also upgrade to producing +$2 fairly soon too. I'm not sure you can really justify removing Salvager either, especially in Seaside with all the duds like Navigator and Pirate Ship and the cards everyone seems to hate like Lookout and Ghost Ship.
Sorcerer's Stone (hhelibebcnofnena)
I'm a bit surprised nobody else went for Alchemy, although actually upon reflection I'm not really. Hilosopher's Stone is of course an awful card that should be replaced. A card that slowly gets better the more you play it is a decent one, although this seems exceeding slow to me. The potion cost slows it down and you need to play 6 Stones before it can match Gold. I don't think taking an Elixir really needs the once per turn restriction either. The big issue is that Alchemy only has 150 cards in it, so if you're using 60 of those card slots for Elixirs then along with Potions eating up space that only leaves enough room for about 5 Kingdom cards or something.
The winner is...
Gubump's Farmer, when I read Farmer I thought "how didn't I think of that?" it seems like a very obvious fix while keeping true to the removed card.
Runners up: Asper's Thimberlig and Commodore Chuckles' Refinery, I liked these a lot too!