My parents have a 93 Beretta 4 cyl. It seems to have an ABS problem but not sure. When you drive the car, most of the time it brakes fine. Every once in a while it when I hit the brake pedal, (and it's usually a second AFTER I press the brake pedal when it does happen) the brake pedal goes just a LITTLE farther to the floor and it make the grinding/pulsing sound that ABS brakes when they kick in. However there is no reason for the ABS system to kick in since it's dry and 90 degrees. And you can hear the "sound" coming from the master cylinder area, but it definitely sounds like the ABS is kicking on. But, the next time you hit the brakes, everything is fine again. Or if you're braking long enough, sometimes the ABS kicks in like the car is on a slippery surface, and then will kick off as if the car is no longer on a slippery surface. If that makes sense.

I have taken off all the tires to look for any leaks. I discovered the rear passenger brake was leaking. The wheel cylinder wasn leaking. I replaced both wheel cylinders and bled the brakes. The brakes seems to work better, however the ABS intermittingly turning on still seems to happen.
Thanks for any help that you can offer.

There may be a sensor that is "seeing" an intermittent signal. If that's the case, a shop with the appropriate diagnostic scan tool could monitor data during a road test and determine exactly what the actual problem could be.
Call around your area or ask people you know where they take their car's for service.
Ask about diagnostic fees and warranties.
And, ask about technician credentials.