What is the value of a one dollar gold coin no year?

It depends by what you mean "gold coin", if you mean a Presidential 'gold' coin then it could be a mint error and worth several dollars if it legitimately has no edge text. However, beware of people simply filing down the edges.

However, if you are talking about an actual gold coin, such as a pre-1933 gold US coin, then the value changes a lot depending on condition, but I don't think it would be possible in the minting process to have a yearless gold dollar unless the date itself was worn down due to excessive circulation.