How did you damage your shoulder?I used to do tons of dips on tricep day. I would do weighted dips and body-weight only dips.
Now, I can't do it at all. My shoulder is damaged on the inside. The saddest is when you can't do an exercise not because you don't want to, but because you can't.
I still do pull-ups. that's my main back workout. I mix up narrow grip and wide grip.
Sometimes, I'll change it up and do bent-over barbell rows or cable rows.