Yes, you can use fixed value capacitor, but your receiver/transmitter will work on a fixed frequency. You will have to take some trial and error to get it to work (most of cheap capacitors could have capacitance differ up to 50% with the same nominal value, pretty much same for inductors).

Actual value of capacitor and inductance define your frequency. For LC circuit resonant frequency is defined as

w = 1/sqrt(L*C)

So, take frequency you want and calculate the value of capacitor for it.