How much gold is in a Zachary Taylor 1.00 coin?

None. Except for a handful of special pieces minted for museums, every one of the roughly 2 billion "golden" dollars minted since 2000 is made of manganese brass.

If you think about it for a couple of seconds, the price of gold has bounced between $1000 and $1500 an ounce. A "golden" dollar weighs a bit more than 1/4 oz so if it were gold it would be worth at least $250. Not even the most boneheaded government bureaucrat would authorize minting coins worth 2 or 3 hundred bucks and then have them put into circulation at $1 each.