I wonder if lowering the coaches Ambition rating would do this? I don't think it would help with his salary demands but he might be less likely to leave.
If not maybe a loyalty rating could be added that would make him stay and ask for more money? Or adjust the ambition rating to work like a loyalty rating.
I'll set ambition ratings lower for guys that have been at the same school a longer period of time the next mod update. But I won't have a lot of time to test so I'll need feedback of how it works out.