We are currently teaching Jackson how to use a sippy/straw cup and he doesn't have a strong swallow either.
We see a feeding therapist and I would recommend finding one if possible. She has given us so much useful information to help with drinking & eating.
We were told water is the fastest flowing liquid and for babies with an uncoordinated swallow they probably cannot react fast enough to swallow it. Now we put things in his cups like smoothies, pediasure or yogurt. It flows slower and he has more time to swallow it before it comes back out. However he still dripples most of it out. The FT said to keep trying, it's just going take time.
She just recommended the following cup for us: http://www.talkingchild.com/Store.aspx?ItemID=52
She thinks learning to suck through a straw will help his coordination vs a nippled sippy cup.