When it comes to watering morning glories you should let the soil dry out in between waterings. What color are the leaves - have they yellowed?
Are they in containers or planted in the ground? For tips on treating over-watered plants in containers, please visit the following link:
One thing is for sure, however. If they have in fact been over-watered you are going to want to hold off on using your watering can for awhile.
For more information on caring for morning glories, please visit the following link: