Here's some other threads where handicapping has been discussed:
http://forum.dominionstrategy.com/index.php?topic=95.0
http://forum.dominionstrategy.com/index.php?topic=950
http://forum.dominionstrategy.com/index.php?topic=1288
http://forum.dominionstrategy.com/index.php?topic=335
Can we maybe discuss it here anyways, since those are all 6+ years old, and several of them are more about handicapping yourself against a weak player, rather than competitive play compensation? Also one of them doesn't have any discussion at all.
Breezing through those 1 page threads, I didn't see anyone talking about non-coin tokens.
For instance, if the second player was given a +action token, or +buy token, to spend once per game.
Or maybe a token that can be used once, as a +buy OR a +action
If those are too much, perhaps require the user to spend some resource to activate it.
For instance, the token could require spending a buy, action, or $1.
those seem less useful in the early game, where you really don't want one player leaping ahead of the other, and there shouldn't be a time when they are backbreaking.
Alternatively, there could be an event that has some small bonus, but it is reserved for only the second player...but as soon as the second player uses it, then it's reserved for only the first player, and control continues to swap with use.
Given that dominion is a game of changing kingdoms, it could be interesting if there were MANY tiny boons to the first player, and one got randomly selected as the 2nd player boon.
I feel like missing an opening turn is too big...
Well, instead of a nerf for the first player, how about a buff for the second player? The second player gets to start the game with the worse half of their deck in the discard pile so that they never have to draw it until they reshuffle it in.
Is that definitively a buff? It sounds interesting, but their first reshuffle only has 1 card better than copper.