Hi,
The ACS AEM Commons Syslog integration depends upon Logback which is part of AEM 6.0. It might be possible to upgrade just the logging subsystem in an AEM 5.6.1 instance. You could also request a feature pack from DayCare for an update of the logging subsystem.
The other option is to use logger, which is a general purpose command line utility to write entries from a file into syslog. See http://linux.die.net/man/1/logger and http://blog.logrhythm.com/uncategorized/using-logger-to-send-file-data-to-syslogd/ for more information. Obviously, the direct integration provided by Logback/ACS AEM Commons is easier to manage, but logger should work as well.
HTH,
Justin