Hi there, I don't know about tropical climates but I do have ~20 goats here in a temperate climate rainforest, and they are thriving. The first generation came from a drier climate, so they did take a few months to acclimate...but so long as they have a
shelter and dry bedding, they generally don't have problems. Of
course like any ruminant they can get scours right when the rainy season starts (from the sudden excess of green vegetation) but usually it only happens to weaker ones and the herbal remedies that I use clear that up immediately.
I will say that it is quite different to keep goats in a rainforest than in the more arid climates where they are usually found. For one, they are like cats in rain and have learned to predict rainfall so that they can seek shelter in advance. Besides being a useful alarm for me (when I see them headed for their barn I know to run! LOL), it can cut into their grazing time during long rainy spells. So if it is a heavy rain day, I make sure to bring cut brush to them or throw out some oats so that they don't get behind on their calorie intake. They can also get fungus in their hooves if they stand in a wet area too long, again, I do deep bedding for them and always make sure that it is dry.
So far as breeds, mine are Anglo-Nubian, Malagueña/Costeña, and Murciano Granadina. I am allowing the breeds to mix and believe that in a few generations I will have a solid meat-milk breed that is a good browser, sweet-tempered, and resistant to humidity and cold. I believe that you could do the same with pretty much any breed; they just need to be well-cared for but not too spoiled and have access to a variety of browse. Animals adapt quickly to whatever environment they're in. I have far more faith in proper care of animals than I do in any specific breed.
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