Not being sure of what back problems you exactly have, it may not be a good advice, but I'm still going to give it
I have problems with my lower back, that made doing situps extremely painful (but it's alright, as they're not good anyway) so I tried another way of working my abs, that didn't involve such a strain on the back. I tried the first method described here
, and it seems to work, because I can really feel my abds "working", as well as not hurting when it comes to the back.
If you want, you can also have a look at this page
, it's a "Abds FAQ", perhaps you can find another exercise that suits you there.