You can use a paintbrush to spread Roundup on the morning glories and just get rid of this weed. I've heard that morning glories store energy in their leaves so try pulling the leaves off when the plant appears and see if that starts to kill them off. Good luck!
I just read Gaia's Garden: A guide to Home-Scale Permaculture. (Wonderful book, by the way.) The author mentions how frustrated he was in trying to get rid of morning glories, and how he did get rid of them: I'd try this approach: improve the soil, and keep approving the soil. You want to improve the soil anyway, right? And if this'll get rid of your unwanted morning glories without requiring the use of some nasty pesticide... well. Sounds good to me!
