What icing will stay stiff (even in tropical heat) after the cake has been decorated?
The ingredients that make icing creamy and give it the bulk for piped decorations, tend to be items that will go softer in heat (butter, shortening, egg whites, whipped cream).  A glaze might set up if you made it sufficiently thick, but it wouldn't allow you to do anything like pipe borders.

While I know it's not really a solution to what you want, your best options are probably to decorate with non-icing items like fruit or candy.  Probably the closest imitation would be to try using marzipan, which can be molded and coloured and I think would probably hold its shape better under heat.