Compressor cycles on and off

OK, as usual, what are we working on, AKA model year, and is this a factory setup, vintage "knee knocker" or modern "Vintage air?"

How do you know the freon is "full" you charged it by weight?

Some of these systems had a stat with a probe in the evap. If that stat starts to go bad this can happen.

The low pressure switch can be bad, or............

you could be low on refrigerant, or............

you could have a problem causing a restriction in the metering. This includes mechanical problems with the metering valve itself, as well as WATER in the system which will FREEZE

If "we" are going to look at a diagram which shows your exact system, we need to know "what" exactly you have.

Have you looked at it with a gauge manifold? What does the suction pressure do?