If this was said recently, it probably means $10,000. There are other slang meanings of 'dime' ('a certain amount of drugs' or 'a very attractive woman') but $10,000 is probably the meaning here.

It seems that the speaker is hoping that someone will donate an amount of money. The phrase "put you down for" means that you are agreeing do give or do something. "I'll put you down for the hot dog buns." means that the person is expected to brings hot dog buns to a barbecue.

I've never heard that expression before, but I would assume it means that person A is asking person B if they would be willing to commit a dime to buy something.