What weather resistant, non aluminum quad cable can I use to run an overhead line to a 220V 20 amp subpanel?
You'll need to field assemble this

You will need to field assemble the correct cable for this job from a few different parts.  First, you will need a messenger wire, made from stranded steel (yes!), to provide this assembly with the mechanical strength needed to withstand the rigors of being out in the open.  Second, you'll need some 10-3 UF cable, just like the stuff you'd stick in the ground for this circuit.  Third, you'll need to use a wire to lash the UF cable to the messenger out in the field.

Once this is all installed, with the messenger wire going up first and tensioned correctly according to a sag and tension chart or corresponding sag and tension calculation, followed by the UF and field lashing (don't forget the drip loops on the UF at each end!), you'll then need to run a split bolt and 10AWG bare copper ground wire down from the messenger to a junction box at one end, where it can be connected to the circuit ground wire in order to bond the messenger wire.