Cap room has nothing to do with coaches salary pool. I think the coach money comes from attendance but idk for sure. The thing to do is what's already been said, hire some young position coaches at cheap contracts and spend big on a HC.
If you have no money for coaches, then find one of your high salary position coaches and fire him, replacing him with someone young and cheap. Coaches are not a huge factor in the game. Yes they influence player development some, but like Smirt said, the HC is the one who matters because of his playbook. The position coaches aren't much more than window dressing/a pool of candidates to promote from within.
I like hiring position coaches whose arrows are pointing up (coaches have rating swings just like players) and have them develop. In later years when HC's and coordinators retire, you'll be able to promote from within rather than poach.