How can I change my population's political preferences?

The only real tool to influence your populations ideology you have is to spend a national focus on the party loyalty of your choice. This is fairly slow and as it costs a national focus slot very expensive.

Otherwise, you pretty much have to encourage people into the pops you want, i.e. capitalists are usually liberal, aristocrats are usually conservative or reactionary; etc; try to create a state, which conforms to the ideology you want.

Keep in mind though, that as long as you are a monarchy, you can simply decide what party constitutes your government. The game is designed to give you few tools to influence the ideology of the broad masses, but most countries can simply go against the wishes of the population.