What type of soil is needed to make the melons sweet?

The warm kind ;)

Well, we've got plenty of that here :) so the melons should turn out sweet! I looked today and saw a couple of flowers on them, Yeah! I can hardly wait!

don't water them in the last 3 weeks for maximum sweetness, as sunny as feasible, and the more organic matter the better. they are quite reasonable plants.

It has also to do with the genetics.
Some melons/plants produce more sugar in the same soil than others. corn is just one obvious example.You have regular, sweet, super sweet.
So, if you want sweeter melons, plant the variety that is sweet, Of course soil chemistry is also a factor. Another factor is the weather:Day high temp; Night low; humidity; sunshine, etc. I would think that melons like cooler nights. This is generally the case with cucurbitacea.

So , the best bet for a givent location (when there is no way to change natural conditions) is to pick and plant the most sweet variety.

I agree about different varieties being sweeter than others. Also, some soil amendments have trace minerals that can also help raise the sugar levels in your crops.

I read a lovely article on Floridata where a man once injected IV's filled with rum into his melon hoping to get rum drunk seeds for next year! If only this were the case!!