I've had my HP19BII for almost 10years and have managed with a broken battery compartment for about three years by using strong carpet tape...unfortunately the tape gave way today and the last remnant of one of the plastic edges needed to hold the battery cover in place snapped off. New tape on its own was not strong enough to hold the cover.
The battery compartment on the HP19BII is on the uppermost right hand side edge, my uppermost edge of the battery cover still slides into place however the lower edge has nothing left to slide into.
To fix, I have used a small washer and a woodscrew (10 milimetre in length and 5 milimetre head) which I have screwed into the calculator case in the gap where the missing edge has snapped off. I inserted the batteries and held the cover in place whilst I tightened the screw and washer so they overlapped the battery cover but held it in place.
To create the hole in the case, I used a very sharp nail as a nail punch, held the HP19BII in between my knees (to allow movement in case I hit it too hard) and tapped the nail into the plastic until it was fully pierced. I then wriggled the nail around to make the hole big enough for the screw to enter. NOTE - don't use a long screw as it might reach too far inside and damage the electronics.
Works a treat for me! Hope this can help someone else!
P.S. I will try and add a photo, hope that works too!