As a concierge / doorman, should we accept the served papers on behalf of a tenant or can we refuse without worry of any legal trouble?

You should accept the papers.  Doorman service is legal.  If the server leaves them, and says they served you on a service affidavit, the service is legal.  If your tenants never get notice and/or defend cases, they will have default judgments.  Thus, you should take it, and give it to the people.  If a person does not live there, you can refuse it like certified mail.  However, it is up to the lawyer for the tenant to try to undo the service, not you.

You are certainly under no legal obligation to accept service of process on behalf of a tenant.  That said, you are a person of suitable age and discretion with whom a process server can deliver papers to a tenant.  If you refuse service, the process server could justifiably leave them with you and claim that the tenant was properly served.  Although perhaps not creating any legal trouble for you, it might create a legal headache for the tenant.  Better (and more considerate) practice would be to accept service on behalf of the tenant and then immediately call the tenant and deliver the papers to him or her.