Potential Coach

Hi All,

I am in dire need of some assistance. I hope my situation is as confusing as it seems to me, but here goes.

I am a Canadian citizen currently on F-1 status as a Graduate Assistant coach for an athletics team at a the College in the US while pursuing my Master's in Education. I previously completed my undergrad, also at the same institution, with a Bachelor's in Business Administration.

I am currently in consideration for the full-time coaching position on the athletics team. I have looked into both the H1-B and TN visas and they are both very specific to being a "Teaching" position. With that being said, a portion of the responsibilities of being a full-time coach do require teaching a credited undergraduate course to students.

So my question is, what type of Visa is appropriate for my situation? And what exactly needs to happen for this to be possible?