Use Potentiometer to change frequency in FM Radio Transmitter
Varactor diodes appear to be your obvious choice for this type of circuit. A reverse biased diode has obviously a high impedance and that suits any tank circuit but, its capacitance can vary with reverse voltage bias changes and this gives you a variable capacitor that is voltage controlled. A lot of RF VCO's use varactor to control frequency of oscillation. Used em love em.

Here's a few ideas for a colpitts oscillator with varactor tuning: -




Here's a tuning stage for a receiver: -



Taken from here