Unless you are incredily lucky by having a well stocked craft shop in your area, I expect that you will be looking at mail order. Look for "mahogany veneer". Most of the Amazon listings appear to be pre-glued for ironing onto surfaces.
A combination of balsa, mahogany stain (for colour) and wet rot wood treatment (to increase surface strength) from a large DIY store might be the best answer. Finding somebody who stocks balsa (or obechi) sheet locally would be an achievement these days.