I use a J Pole for air band (122 MHz). I get superb aircraft reception but a very weak signal from my local airport 20 miles away. Is there a way to set up a yagi, or other gainy directional antenna, pointing at the airport and combine it with the omnidirectional J Pole ? I assume I'd need to get the impedance back to 50 ohms. Could this be done with a phasing harness ? Would I be able to mount both antennae on the same mast and have only one feeder coming to the receiver. Help appreciated.
They can be combined, but if you are thinking by combining them you'll get the best of each antenna, that's not how it works.
Besides signal, each antenna picks up noise. The two combine to be, in effect, a single antenna with a different directional pattern.
A cheap option is to put the two on a switch, and you can then manually select whichever antenna works best for the situation.
If you want to get more sophisticated, if you have two phase coherent receivers you can write an algorithm which dynamically combines the amplitude and phase of the two for best reception. Such an arrangement is called an adaptive antenna.
Your question is very similar to this one, except decent coaxial cable for the air band is much cheaper than decent coax for 1 GHz.
In addition to the suggestions given in the other question, you might try just mounting the antenna up higher. Or even just a few feet over, because your antenna could be in a local null. You've surely experienced local nulls before—you're sitting at a red light and your FM broadcast band reception is suddenly terrible; then the light turns green, you roll just a few feet away, and the reception is good again.