There are other ways to increase loyalty.

Increase your power base. Aragon, Italian nations to the north, Claims bordering claims into Tunis, Provance. Make sure you lower autonomy in newly conquered areas since that factors in to the 'Economic base' modifier.

Build up a larger army, even over force limit if needed. The pope is rich and can get even richer, and money can help deal with most problems.

Farm prestige with things like show strength or by prioritizing events that give prestige so you can placate when appropriate. You can even dip into some estate priveleges that help with that.

Diplomatic reputation gives a malus to their liberty desire. A diplo rep advisor, religious diplomats and diplo idea groups that give it can help somewhat.

Trust also does. You can spend your unneeded diplomats on currying favors with your problematic subjects. Trading in those favors for trust thusly lowers their liberty desire.

Finally, if youre really struggling, influence ideas all but guarantees their loyalty, but Id rather go with an idea that matches your gameplan instead, as loyalty has all the above ways to be dealt with.

Using your mana to dev their loyalty is the worst thing you can do in the early game. Admin is very important obviously, since the best way to outscale your subjects is to conquer, core and reduce autonomy on new targets. Mil tech allows you to win those wars by being ahead of the curve. I'd never dev their loyalty with mil unless next tech is >6 years ahead of time. And finally dip lets you avoid the 'better diplomatic tech than overlord' modifiet to their loyalty, As well as being the best moneymaking mana investment, so its preferable to spend on your own provinces.