Rugby scores code golf
Python 3, 113 104 bytes

a=int(input());print(['%sK,%sT,%sC'%(i%a,i/a%a+i%a,i%a)for i in range(a**3)if i%a*3+i/a%a*5+i/a/a*7==a])


First attempt at code golf. Brute force list comprehension. I'm assuming the list output is acceptable?

Counting tries + conversion as 7 points removes the if statement. Inspired by xor's python 2 answer.

Try it here