Pushing happens in many places, on your side, on hands and knees, turned around holding on to the back of the bed, on a birth stool, in a tub, using a squatting bar on the bed.... (chicagofamilydoulas.com)
We have a co-sleeper cot that attaches to our bed so the wire goes through a gap underneath the cot, the runs behind the back of our bed so it's tucked out of the way. (ababyonboard.com)
One of the ones that many moms find comfortable is to kneel backwards on the bed and face the back of the bed. (verywellfamily.com)