Is there a way to search for coaches in the last year of their contract? I'm considering hiring a new coach, but I'd like to see who is almost out of contract

Sadly, I don't think there is, you would need to manually go through and check each coach out. If there is a way, I haven't found it.

You need to do a couple steps but it can be done. If you know what type of coach you want, you can go to coach search and look for West Coast Offensive Coordinators. That will tell you who is employed where, then you go to that team's home page and click on their coach list. It should show an asterisk if they're in their last year.

Contracts don't matter for coaches since you can poach. Coaches will take a promotion so you can offer a head coach contract to a currently employed coach (during early free agency only) or coordinator and they will take it.