Here's a simple card inspired by some of the rotating cards in Agricola. (NOTE: it is an heirloom, not a supply pile)
I just made an heirloom without a kingdom pile to go with it. I figured the kingdom pile is unnecessary for the contest, since Gift is the card that gives the player interaction. That being said, I will make a kingdom card to match it if anordinaryman wants me to (maybe i'll give it some more player interaction).
I'd thought I'd go with a card that rotates along the decks. You get a little bonus when you pass it along (i did that or else everyone would be passing them along and it would cancel itself out). You can keep it; of course then it just plays like a copper. This is obviously going to affect the openings a little bit like baker.
1) Your opponent does not gain the card and therefore cannot react (for example with a trader)
2) the card is priced at 0 intentionally. I wanted it to continue to rotate hands so I wanted to disincentivize trashing it. At 0 it doesn't work well for trash for benefit. it also can't be trashed with things that only trash copper (ducat, moneylender). And then, if you really want to get it out of your deck you could always play it as a silver (though it will likely come back).
Update: I have added Research here (this should take care of the heirloom problem and give more interactivity). Here are my comments:
You've worked very hard on your research; too bad everyone wants to steal it for themselves. It's a lab that can be stolen for a cost.
1) The choice of stealing goes clockwise from the current player. Once one player takes it, no other player can take it since it is no longer in play.
2) "Other players" refers to all the players who did not steal the card.
3) Because this is a card that rotates and everyone will end up benefiting from, the cost has to be low since why spend my money if everyone is going to get the benefit (also to prevent tfb). I've also added an interactive clause that allows all your opponents to gain one for free (when you gain your 2nd card). I might tweak this clause since it allows the pile to deplete fast in a 4p game.
4) This pairs thematically well with Gift. Gift is a card you give to your opponents, Research is a card you steal from your opponents.
Update: I have decided to do a different set of cards but with a similar idea. This is no longer my submission.