The advice given in this thread has been good, but I can usually avoid rebellions no matter who the governor is, provided I adjust taxes properly and keep the standard 100-peasant garrison in the province. (This doesn't mean I micromanage taxes; I just lower them when the province is first conquered and then raise them after a while.) To increase loyalty quickly in conquered provinces, I simply convert the populace and build stuff there. I don't like to let loyalty drop much below 150%.

I've never put a great deal of time into selecting governors. I always pick highly loyal individuals. If it's a rich province I try to find someone with 4+ acumen; if it's poor this is not so important. If the governorship gives command stars, I try to reserve the title for a general I'll be using in battle. I don't pay much attention to piety or dread, and even on expert this doesn't seem to pose a problem. It seems to me that the factors that influence a province's loyalty most significantly have nothing to do with the governor.

Of course, my playing style is designed to be less detail-oriented, so that less economic micromanagement is required on my part. This certainly isn't the most economically efficient way to play; it keeps me safe from rebellions but doesn't sqeeze every florin possible out of my kingdom. I'm more careful in the early game, when my kingdom is small and I need more money to survive. However, once the Empire has grown large and is agriculturally upgraded, cash is flowing in faster than I can spend it and I don't need to pay much attention to the details.