Hey, I am new here but I do have some business experience!
Being a gym rat myself I am not so sure if this is going to work..

1. You are limiting yourself - think how many trainers/coaches are out there versus customers who might need to loose weight, train their back due to backpain etc - I guess its 1:10000 or even 1:100.000

2. Most of the gyms have already personal trainers working there freelancers and own stuff - and if you talk to them you will see that business is for most of them not so great.....

3. I used to live in germanys biggest city and saw many gym ideas fail just copy an already successful idea and you are good to go
PM me if you want (what I think is the best idea)