I may be behind but the last time I looked, Nagios was free and there are some Avaya specific plug-ins. Not sure if there is one for the new Communication Manager MIB.
There are so many tools. Even the basic Avaya tools such as ASA have some pretty neat reporting.
SNMP is SNMP is SNMP. You can get SNMP Traps but the key is to be able to filter, sort, and prioritize. There is a tremendous amount of data. Look for these features in any Network Monitoring tool.
You might also want to look at implementing the Avaya Diagnostic Server (ADS) which free (assuming you are on a current release). Just requires an e-mail to Avaya to obtain a license. Does pretty well for looking at voice quality issues.