Attempting to make a balun by coiling coax is a tricky business.
The idea with these baluns is to make an inductor with the coil. Because an inductor has an impedance that increases with frequency, it's hoped they will look like a high impedance to common-mode currents on the coax.
Unfortunately, a real coil also has capacitance between the turns which counters this effect.
Furthermore, this approach does not take into account the common-mode impedance of the feedline, which could take all kinds of values depending on the length and placement of the feedline. Adding a reactive impedance in series with this unknown impedance might actually make things worse by creating a resonant LC circuit with a lower impedance at the operating frequency.
As such, I would first recommend you do nothing. The ground plane already presents a low impedance to the common mode. If the feedline exits below the ground plane and away from the antenna, common mode current on the feedline should be low without taking any particular action.
After installing the antenna, you can measure the common-mode current. See How to detect common-mode currents or “RF in the shack”?
If then you still have issues, you can try adding a balun. And because you have a mechanism for measuring the common mode current, you can find the ideal number of turns by trial and error. If you can't get that to work sufficiently well, you can try other balun designs which may be more suited to VHF.