I guess the way to have it done faster is to spawn some influence starbase near the planets. I think in the manual they say you need 4X more influence than the other civ. You should be able to see if the planet is likely to flip if you can check it's approval rating, if it's getting low, good for you. But for that I guess you need to spend a little in spying.

Ir is posible that the AI race is building alot of Culture bosting impovments, you can almost always overwelm the with Influancer starbases if you want to do the work. How powerfull you can make the starbase is determined how far up the culture branch of the tech tree you are.

Also if that race has any moral resourse it can make it much harder to bring about a flip. If you are at war with the race, or are willing to be, destroy any Influancer and Moral Resourses thay have.

Also, doesn't the number of ships in their orbit limit the likelihood of a flip? IIRC if they have alot of ships in orbit (like most minor races tend to do), it makes it all that more difficult to have them flip.