Try Mr. C's furniture just one block behind the Belize Yacht Club and next to Pedro's Inn. They have floor models available and also custom make hardwood and mahogany furniture. Take a picture from Ikea and they will duplicate it, 95%. Make sure to ask for very dry wood and specify the stain. I prefer sanding sealer to give it a smooth shine and not the varnished look, costs a little more, but worth it.
His carpenter is in but he'll be in El Salvador until the 14th.
Very affordable also.
For US made furniture Mirab's Furniture Gallery offer Ashley furniture in Belize City, they make it easy for you to get it to the island.