I don't think they are toxic, although there is mention of possible diarrhea if the seeds are consumed according to the below-linked site. There are a number of similar sites on the web that have some plants listed and others not, so you might want to consult some other places.

In general, I expect many many millions of dog owners grow morning glories with no mention of problems.

Here is a link that might be useful: ASPCA Poison Control Center