To make use of AppHarbors log drain, you need to create a new log in your existing Logentries account, except choose Plain TCP, UDP as the source. This will give you a port number to use with the log drain as like you mentioned the Token input can't be configured with manual drains. Then on AppHarbor, you would add this url for the drain:
syslog://api.logentries.com:PORT
where PORT is the port number you were given when creating the log. You can create as many of these logs in your Logentries account as you wish and thus point as many AppHarbor sources to the one account as you like. You can give me a shout at support@logentries.com also if you have anymore questions, or here of course if you would prefer to use SO.
Mark