Looks like I need to get new tires for the trailer, on it now are the Carlisle ST175/80D13, Do I need to put that type back on or can I put car tires on it? Any recommendations?

Sorry, won't recommend a brand to avoid the bashing of one brand over another that occurs when this subject is brought up. However, I will step out on car tires vs trailer tires. The stresses on the tires are compleely different between the two (passenger vehicle and trailer) and I think it will be generally recommended to go with tires designed and labelled as trailer tires. You will also hear the "discussions" about radial vs bias ply for trailers. I personally run radials and have not had any problems.
Do some research for yourself is the best recommendation I can give because ultimately the decision and the outcome you have will be the result of your efforts and not based on someone elses which may have been good or bad.

If you put ST (Special Trailer) tires on be sure to find out and follow their inflation pressure and max speed ratings.

Pressure and load ratings probably on the sidewalls - dealer should know or find out the speed rating.

Thanks guys.