Broken battery door latches appear to be a common problem on the Dimage Z1. I did a search for spare parts on this model and the battery door came out at the top of the list. However, the spare part is no longer available.
The best solution might be to use velcro to make a locking strap, as follows:
- Obtain some 3/4" wide velcro tape. Not the self-adhesive type as this is not practical in this application.
- Cut a 4" piece of loop tape (the "fuzzy" part of the velcro) and fold 1" at one end over itself with the fuzzy side out. Glue the end onto itself with a strong flexible glue such as contact cement.
- Cut a 1/2" piece of hook tape, and glue it to the center of the battery cover.
- Glue the loop piece to the side of the camera body, fuzzy side out, in such a way that the folded-over end sticks out over the battery cover, and can be folded over to grab the hook tape on the cover.
The result might not be a work of art, but it's more practical than masking tape.