My dad has cancer, mom has dementia. Where can we find a skilled nursing facility where they can have a room together?

It may not be possible for them to share a room together as their needs will be very different. Facilities have very strict requirements as to who they will admit and under what circumstances.
Dad will need medically related long-term care whereas mom will require a secure dementia unit. If you find a facility that can satisfy both needs, terrific, but the best that will occur will probably be that they will be able to visit and perhaps dine together.