If this is via iMessages then no.
You would have to change the Apple ID being used in Messages and the iOS devices you are using.
IF it were AIM then this has a Privacy tab and you can Block Specific people. (Or Allow Specific people)
Jabber IDs can have th Authorisation to be a Buddy removed.
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously