I used gel antiperspirant for a long time because of this problem, but the downside is you have to wait for it to dry or you'll feel it under your pits all day long.
Ther are quite a few 'invisible' brands that are marketed directly to fight this. I know Secret has one.
I also really liked the kind you had to 'click' up and it'd spoot out of the little holes, you'd rub it on and it'd dry pretty quickly.
Just look for something that says 'invisible solid' on the packaging.