Yes, varicaps are good and there are even varicaps with very large capacitance swings exactly for this purpose.
But it does require a very steady voltage and many more parts than just a single passive to not accidentally load the resonant circuit to the point that it becomes ineffective. You need to de-couple considerably to make this work, especially without injecting (phase) noise. And frequency stability and phase noise can be extremely annoying in particular applications.
That’s why you probably want to use it in an oscillator rather than a filter. Then some of those problems go away. Although, some new ones appear like having to add a mixer … Some time ago I thought making a double superhet would be too complex but apparently it turned out quite a nice DYI project.