All the data for all sites is in the same database. If you can't get a backup of the database I have no solution for you. That is something people need to understand before they choose to host multiple sites in one installation.
I don't really recommend hosting multiple customers in one installation but some people do it, it is a business decision they are free to make. Myself I would only host multiple sites for the same customer in a single installation for this very reason that the data is all in one db.