I would recommend reviewing the threads on CUs here to get the details of what credit score, etc. would be optimal for apping and getting accepted.
If you can move foward, I would recommend four good options:
Good luck on your journey!
CCCU gave me a card with history of BK.
I also got a secured cc with CCCU last March with the tail end of a bk. It is due to drop this July. Also, I just got an installment acct from them and they did not do another hard pull. They said that the inq from March was good enough for them. They are great to work with and they are close to home.
A strategy that is helpful is to talk to the lo once or twice and explain your situation, if needed. Others have done that to good success.