Just change the table prefix in the wp-config.php file of the second installation.
For example, I do this for student club blogs at a school site I run. Each club uses the database ‘wp-clubs’ but each club’s blog uses a different database prefix. Eg: ‘astro_’, ‘nature_’, ‘writing_’, ‘chess_’, etc. Everything in the wp-config.php file is the same for each except for these prefixes.