Measure length of your coffee table height. You will want the height of your final coffee cart to be about 30 to 36 inches from the floor. Most coffee tables are lower, knick-knack tables or lamp tables are usually the height you need. Save yourself time and find one of the needed and proper height.
Also, coffee tables work best because they most often have the upraised lip on the table edges. Claw feet work best on legs because there is enough room on the bottom of the legs to install casters.
Make leg extenders if necessary. Remove table legs from second hand table. Cut necessary height leg extenders from 2 x 2 wood pieces. Sand smooth and screw to underside of second-hand table where legs were removed. Apply carpenter's glue before screwing. Use screws into pre-drilled new holes, not original leg screw holes. Let glue dry completely.
Join extenders to original legs. Drill hole in center of leg extenders and removed legs to reconnect removed legs to extenders. Make holes 1/2 inch diameter to receive steel stud connectors in each hole in extenders and matching holes in original legs. Place epoxy in extender holes, insert steel studs, let epoxy dry in extenders. Place epoxy in matching leg holes, insert steel studs, let epoxy dry in legs while being clamped with wood clamps. Protect leg and extender wood from clamp damage with scrap wood. Remove clamps on legs and extender joints and sand all surfaces smooth.
Finish coffee cart. Sand all surfaces smooth (if necessary). Wipe or brush matching stain color on all sanded or unfinished wood surfaces (leg extenders) and let dry completely.
Install casters on claw feet. Drill hole size needed to insert casters. No metal inserts are necessary but you have an option to provide some if caster manufacturer provides them. Clean holes by blowing drill sawdust out of holes. Insert removable caster pins into drilled claw feet and turn legs over. Your former coffee or knick-knack table now becomes your new homemade coffee cart.