You can use the getTables() method of the DatabaseMetaData interface to retrieve a list of tables:

String connectionString = "jdbc:myob: If using an online instance: InitiateOAuth=GETANDREFRESH;OAuthClientId=YourClientId;OAuthClientSecret=YourClientSecret;CompanyFileId=yourCompanyFileId;CallbackURL=http://localhost:33333;User=companyFileUser;Password=companyFilePassword; If using an on premise instance: InitiateOAuth=OFF;URL=http://localhost:8080/accountright;CompanyFileId=327eed10-9615-4e5e-bd9e-ae2cc00e2c70;User=companyFileUser;Password=companyFilePassword;";

Connection conn = DriverManager.getConnection(connectionString);
DatabaseMetaData table_meta = conn.getMetaData();
ResultSet rs=table_meta.getTables(null, null, "%", null);  
while(rs.next()){
  System.out.println(rs.getString("TABLE_NAME"));
}

The getTables() method returns the following columns: