What icing will stay stiff (even in tropical heat) after the cake has been decorated? I live in the tropics and every icing that I've used melts on the cake if it is not refrigerated. Is there any icing at all that will stay stiff once I ice the cake with it? I would like to be able to pipe borders, etc without the icing just melting off the cake. Traditional butter-cream and royal icings just don't work.
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.