I got below reply from BMC:
Unfortunately, there is currently no option to enabled the Copy button in Self Service for a specific profile. At the moment the only option is to enable/disable the copying of incidents in Self Service is the "Allow clients to copy Incidents". We recommend that you submit an idea on the Remedyforce Communities site for the feature you would like on making the Copy button enabled in Self Service for specific profiles. This idea will allow other customers to vote on the idea as well as bringing it to the attention of product management. If the idea has enough votes product management will consider it for a future release of Remedyforce.