All the trainers I have ever flown will do a loop, not always pretty but they will do it. A lot depends on prop selection, wind and pilot skill. Even a slow dog of a trainer will do one if you dive it first. I had a 12 year old student that decided we should fly in really strong wind, I never tell a student not to fly in the wind, even heavy wind. The trainer I had was an old Tower that had been repaired a lot with a really worn out OS 40la. I took off and let the kid have it on the down leg and when he turned into the wind he freaked yelling dead stick. The plane just stopped. I told him to push down and then the plane started flying again.
I took the plane over and put it into the wind and just pulled full up elevator and that plane just staid in one place looping.
Any good instructor can teach you all these little tricks to get a plane to do things it isn't designed to do.
I love flying trainers.