During the offseason, in the most ridiculously stupid move, I managed to fire my HC while trying to add a QB coach. In some ways, I'm OK with this because my DC is almost as good as HC as my former one. The problem is I can't figure out how to promote my DC to HC. Is this possible?

That is promote a HC without the coaching being in his final year of a contract?

http://cust28.myfootballnow.com/community/3/1076?page=1#6822

But that's not what's going on in my case. DC to HC should be a promotion and not a demotion. I think that what happened is that I just signed the DC. It's OK because my OC is almost as good as the DC and has the playbook I want, so I can work on promoting him instead.

Thats kinda strange. Did you give a new contract to your DC giving him the Head Coaching job ?
The only ways your HC would be fired is if you give a new contract to another coach giving them the Head Coaching job or if your HC contract expired.

No what I did was more stupid than that. I went to hire a new QB coach. Somehow I hired him to be the HC instead, which was hilariously stupid but also just hilarious since he's an HC with a 197K contract. During the same spin, I hired a new DC to replace my old one. I would like to just slide this new DC to HC, but I can't figure out a way.

I don't think you can offer your new DC a second contract in the same year.

That's what I assumed. It's OK. My OC has the playbooks I want anyway.

This is correct - a coach cannot sign two contracts in the same year.