How do you compress the piston back into the caliper without having to replace the caliper?

Since you did not give any details I will have to answer with some general suggestions.

1. standard caliper, use a C clamp to compress the caliper ( no need to bleed system )

2. If you do not have a C clamp, release the pressure by turning the bleed screw and push the caliper in. you will need to bleed the system if you do this.

3. certain vehicles need a special tool that turns the caliper in ( will have a slot in the piston ), they are pretty cheap and your local auto parts store will have them. When you get there get all over the parts counter person for not mentioning that you would need one.