Unpopular opinion time! I find it hard to design a card for this, because many of the existing cards just play better if they're not part of a split pile. The submissions so far reinforce that opinion for me.
This goes on top of Cobbler. I love Cobbler and I want it to be better. The Boot token would make it much better in most kingdoms. There is only one Boot Token, so the price reduction applies to everyone. (Pretend the card says "Action-Duration" on the bottom. Looks like I forgot that part)
I'm not sure this makes Cobbler better. Cobbler is an early-game card, and with this you can only gain it well into the midgame.
Here's my entry this week. 5 copies of Lockbox go on top of 5 copies of Treasurer. +Buy helps deplete the top half of the pile, and then once you get the Key from Treasurer, you can "unlock" your Lockboxes for an extra one-shot $3 each. Be careful though: your opponent can swipe Lockboxes from the trash for themselves, but they'll need to steal the Key from you too to activate them.
This makes the first option on Treasurer pretty useless, by buffing the other two and limiting Treasurer gains to the mid-late game, where trashing is less useful anyways. I also really don't think it's necessary to reward Key control more. The better design for this would be if the text that Lockbox has was on Key, and Key did nothing else, and the first Treasurer option was removed. But of course that doesn't fit the contest.
Scrying Bones - $2
Action
+2 Cards
+1 Action
+1 Coffers
Put 2 cards from your hand onto your deck.
A cheap Candlestick Maker variant that can set up Mystic and helps you find the Mystics. It is an even 5 and 5 split with Mystic. Not sure if the draw 2 cards then return 2 cards effect is equivalent to a +Buy, but pricing it at $3 does not seem very appealing, so I went with $2. This also goes great with a number of other cards that care what is on top of your deck. Feedback is appreciated.
Giving Mystic an inbuilt combo cheapens the experience I feel. Now you can't enjoy those times when there are other combos, and much of the deck-tracking rewards from Mystic are gone.
Goes on top of King's Court
This should probably have a ? in the top corners, as the $4 is conditional (see Charm). I'm not convinced that this is good enough for King's Court to be uncovered a signficant portion of the time. Even if it is, though, limiting to 5 King's Courts makes it likely that the person who wins the split has a massive advantage.