What recourse do I have for service of summons to a defendant who can't be found?

If Tennessee is like the jurisdictions in which I practice, there is a procedure for these situations where the Court can authorize another method of service, perhaps by mail, or by publication in a local newspaper, if you can demonstrate that you are  unable to effect service in the normal ways.   BTW, presumably this guy drives to work.  Even if you can't get into his place of business, you may be able to serve him in the parking lot when he arrives at or leaves work.  Also, you should check the rules on service in Tennessee.  It may be sufficient to serve a person of suitable age and discretion at his last known address, or at his place of employment.  In other words, in New York, it would be good service if you left the summons with a person of suitable age and discretion at his place of business and also mailed a copy addressed to him (in a plain envelope) at the same address.  There is no requirement that you hand the summons to the defendant himself.