After hours of searching and looking through the code of Taps, I found the answer myself :D.
The problem is native SQLite in JRuby is a madness, we must use JDBC instead.
export TAPS_DATABASE_URL="jdbc:sqlite:///tmp/taps.db.2012-08-07"
taps server jdbc:sqlite:///my-db.sqlite3 user passwd
The first command is to prevent Taps from creating it internal DB with native sqlite connection. Taps will use ENV['TAPS_DATABASE_URL'].
In the second command, we must add a prefix 'jdbc:' to instruct Taps (actually Taps use Sequel) connect to DB with JDBC adapter.