Although it is a slightly archaic law, I believed that it is still illegal to own gold bullion in Belize. It stems from an old British law. Consequently there is not a lot of chance of there being a precious metal dealer. As a matter of fact, until 1974(?) an American could not own bullion without a license and I think it was even later in Canada before the law changed.
I am a bit of a numismatist and have travelled the entire country at least twice and I have never heard of a coin dealer anywhere. In all honesty I was never really looking. I have bought a coin or two from the vendors in the market by the bus depot in Belmopan (over paid though a nice keepsake) but that was awhile ago. The Central Bank of Belize does put out commemorative coins, which include a few gold coins. Some that I have seen are the Battle of St. George’s Caye coin, the $100 dollar gold coin, and the Mayan artifacts series. Unfortunately I do not have any of these. I don’t know but and I am guessing but I would think that the economy would not support a coin dealer???