Your target number on the Pope-o-meter is 10. Try to keep it there. 9 is ok, providing nobody else is as high or higher. At 8, bring it back up. There are a few ways. Building churches raises it, but how much depends on the size of the church. The only big jumps are cathedrals and huge cathedrals, which seem to give you a full point on the scale. Getting a priest into the College of Cardinals raises it, which is hard to do as England but possible. Completing a crusade raises it, not something you can do every turn of course, but possible. However, the best way is to park a diplomat near Rome and hand over the payola every so often.

You want Catholic high and heresy low in every province, so you need a lot of priests. Build a cathedral as soon as you can, and train all your priests there. If you can build a Theologians Guild there, do so. The guild will give the Orthodox Instruction trait to all priests trained there, which is good for +1 piety. The cathedral will make all priests trained there Bishops, good for another +1 piety. It may be a bug, but in my spanish game when I upgraded the cathedral in Leon to a huge cathedral, I LOST the +1 piety on new priests. I was expecting to build ArchBishops, but no dice. I didn't even get the Bishop trait any longer. Whenever heresy pops up, move quickly to quash it. Dump several priests into the province until it goes down.

This is what I've been doing in my spanish campaign. I'm 110 turns or so into it now, and I've yet to have any characters so much as targeted by an inquisitor. Only once have I seen an inquisitor doing anything in my lands other than passing through. Last night one stopped near Toulouse for 3-4 turns, but I had a family member in the castle, two cardinals and a bishop in the province (heretics keep wandering in from Marseilles and getting executed) and another general leading an army in the region, but no attempt to denounce any of them. It costs money to stay on the good side of the Pope, and I spend it gladly. Of course, having 11 out of 13 members of the College of Cardinals doesn't hurt.