The 1860 is not a super common date for the gold dollar, but the P-mint example is relatively inexpensive despite a mintage of only 36k. The Dahlonega minted coins are very rare (3.4k minted), and the San Fran minted coins (13k) about midway between the two.
Expect to pay quite a bit for a nice mint-state example of any of them, but some persistent looking (and perhaps visiting a regional show) should be able to turn up a nice circulated example if that's what you're after.
I suspect that it will not be an easy coin to find, particularly in undipped and uncleaned condition, but with patience you should be able to find one.
If you are looking for a high-end one, Doug Winter's one of the best:
http://www.raregoldcoins.com/inventory.asp He doesn't have any currently, but if you contact him, I'm sure he'd take a wantlist from you.
If you are looking for a more affordable circulated example, I would suggest you reach out to Rare Coins of New Hampshire.
http://www.rare-coins.com/ They don't have one now, but they too will take wantlists.
Good luck, and please let us know if/when you find one!..Mike
