I know that in most circuits you use a tank circuit consisting of an inductor and variable capacitor in parallel to generate different frequencies like this one. However since most cheap trimmer caps are not very user friendly(have to use screwdriver to adjust instead of traditional knob) I wondered if there was a circuit that somehow used a variable resistor to change the frequency. This circuit would be less than 12 volts. This circuit doesn't use of variable cap could I mod it in some way? Any ideas?
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