Appeon supports Dynamic transaction object to data source mapping, you can create two data sources to connect different database. Please refer to the following steps:
1. Add data source pointing to different database in AEM;
2. Follow below online help documentation to setup transaction object to data source mapping using dynamic transaction in Appeon Web Application rather than doing it in AEM.
http://www.appeon.com/support/documents/appeon_online_help/2015/server_configuration_guide_for_net/ch03s05s01.html

You can modify code like SQLCA.DBParm="CacheName='ASADataSource1'" to connect different data sources.
ASADataSource1 is the name of a data source.
and please use the correct SQLCA.DBMS based on your database type.

For example: 
SQLCA.DBMS = "ODB-ASA"
SQLCA.AutoCommit = False
SQLCA.DBParm = "CacheName='appeonsample'"

connect;
// your script


/////////////////////////////////////////////////////////////////////////
disconnect;

SQLCA.DBMS = "ODB-MYS"
SQLCA.AutoCommit = False
SQLCA.DBParm = "CacheName ='appeonsample2'"

connect;

// your script