To tune a circuit you have to adjust its resonance frequency, as you say the easiest way is to buy a variable capacitor and use that. The other way is to use a fixed capacitor and use a variable inductor. Select a capacitor near the middle of the range offered by the correct one. The circuit should now be tuning too high, so squeeze the turns of the coil together to increase the inductance, or spread them to reduce. A good little too is to have a plastic rod, with a little piece of copper melted in the end and a slug of ferrite on the other end. Putting the copper end into a coil will reduce its inductance, using ferrite will increase the inductance.
Frank