If you have access to a computer with the same platform as your ISP, you can install DBD::SQLite locally and then FTP the results into place on your ISP.

If you want to stick with DBD::AnyData, you'll have to escape the data before inserting with s/\n/\\n/g and then unescape it after fetching with s/\\n/\n/g

If your host has BerkeleyDB or DB_File or something better than SDBM_File, you could also use DBD::DBM which wouldn't require additional compiled components.

You might also consider things like kwiki or bryar which can manage content using the file system as a database and which don't require AFAIK any compiled components.