I live on the edge of the rain forest of Puerto Rico. Haven't had problems with roaches, but the only way to solve the humidity problem is with a dehumidifier. You should be able to get them at a local Sears; or they can order them for you. Depending on how large and how well sealed your room is, a 55 pint dehumidifer should probably do the job. My darkroom is about 10x10 feet with a 10-12 foot sloped ceiling, and a 55 works great for me.
That said, you will also need an air conditioner. To control fungus, you need to maintain a temperature below 80F and humidity below 50%. I run my window AC during the daytime in the summer, but don't need it as much in the winter or at night. The dehumidifier shold use about half as much electricity as the AC, but won't cool the space.
Trust me, you need the dehumidifier. Dessicants and other moisture absorbing products are no substitute. We also run a smaller one in our walk-in closet to keep our clothes fresh and dry. It's wonderful.