I assume that you want to charge or discharge the capacitor a lot faster than will get it just charged each half cycle.
So I guess that the capacitor should be charged or discharged in about 100 nS. The charge is 5 nC (5 V * 1 nF) so the current is 5 nC / 100 nS = 0.05 A or 50 mA.
The output current of the inverters that you are using will be in their data sheets, and you need enough in parallel that they will provide 50 mA
Even at 10 mA, you should get the full output, but the waveform will be very much a triangular one.