Building a sphere of influence is not something you slowly do by influencing a country, instead it happens by event. As a part of this great powers will be able to stir up revolts in smaller countries. A communist country may stir up a communist rebellion for instance - of course pops are still of importance, turning a democratic country communist or fascist when things go well will be hard. Rebellions may come into existence organically as well and great powers may even meddle in domestic affairs of other great powers. Democracies will set up conservative-minded dictatorships. By trading and building up a friendly relationship, countries that have a similar government may also slowly (and peacefully) fall in your sphere of influence, but it's no longer done through spending diplomatic power directly into building up influence.
About rebellions to bring countries in your sphere:
- Conservative and liberal democracies will set up conservative dictatorships, though they may support a democratic movement as well if one is active (started organically) (and this will be cheaper)
- Socialist democracies will set up progressive dictatorships, though they may support a democratic movement as well if one is active (and this would be cheaper)
- Conservative dictatorships will set up other conservative dictatorships
- Progressive dictatorships (Modern-day Venezuela-esque for those wondering) will set up progressive dictatorships.
- Communists will spread communism.
- Fascists may both support conservative dictatorship or spread fascism.
Countries in your sphere that have an incompatible government:
- Democracy-great power + Democracy/non-radical dictatorship
- Non-radical dictatorship-great power + non-radical dictatorship
- Radical-dictatorship-great power + Radical-dictatorship OR democracy with radical party in power
then your influence will slowly leak away...