What would cause the engine in a 1992 Chevy S-10 to overheat only when you use the Air Conditioner?

This is an early sign that your radiator needs to be flushed, or replaced. I would get this done to avoid having to drive w/your heater on during these hot summer months. Probably the radiator is marginally blocked or the thermostat is sticking partially closed. Somehow the engine is not getting enough coolant flowing. If you've never had the radiator removed and tested, now seems like a good time. You don't say if you are driving down the road or not. If you are driving down the road there is suppose to be enought air pushing through the AC and radiator to keep everything cool. When you are parked or in slow traffic the electric fans come into play. The electric fans on the radiator may not be working. They are supposed to come on and draw air through the radiator and AC condenser at a certain engine temperature. There are sensors and the car computer involved in this process.