A simple home-made antenna will work better than any discone...provided you "tune" it for the required frequency of operation.
For a frequency of 120Mhz (somewhere near the middle of the airband - you can of course use a more specific frequency like your local tower or approach) the wavelength is 2.5 metres...give or take a few mm
A simple half wave dipole, resonant at this frequency, can then be constructed using a length of wire just 1.25 metres long.
Cut your length of wire in half and attach it to a suitable length of dowel (or similar). Attach a length of 50 ohm co-ax to the centre point (where you made the cut) ...making sure there is about an inch gap and that there is no short circuit.
Attach a BNC connector to the other end of the coax and you're good to go!
Any book (or website!) on antenna theory will include diagrams and probably better instructions. I use one of these and it really pulls in those stations that would otherwise be down in the noise!
You can do it!
Dean (qualified ham radio op. G0RIF)
Life's dangerous. Get a f**king helmet!