I looked into this a great deal when I had my band, initially I was told by the nursing staff to avoid doing sit ups/ab crunches for a few weeks. When I started hitting the gym at weeks 5 onwards, I experienced a great deal of pain, so much so that it took us a while to figure out it was because I had been using an abdo machine which is just like doing sit ups! The main man at our provider doesn't recommend sit ups for anyone with a band as it can cause tenderness around the port area, swelling and isn't recommended. I have tried doing similar exercises since and have found that it does flare up again if I try.
All you can do, is speak to your provider. My own says avoid (although i can do side waist bends) and I follow their guidance, but be aware that some exercises can cause issues and at the very least they also say such ab crunches and exercises need to be avoided with the band for a good 6+ weeks post surgery.
There are other exercises that you can do which will help which aren't direct sit ups etc, depends whether you think any potential risk is worth it.
best exercise . . .walking! Aim for 10000 steps a day.