Armenia became member of the Council of Europe on 25 January 2001.
http://hub.coe.int/
Armenia is at the border Europe -Asia...
Geographically, Armenia is on the Asian continent. It is situatred north-east of Turkey and south of Georgia. It is considered a Eurasian country but its participation in the European Council does not make it European.
Yes, it might be member of COE, but it is closer to Asia both geographically and culturally.