Is there a putative father register here in Tennessee so the father can be easily contacted if the mother wants the child adopted

Here you go.

36-2-318. Putative father registry. (http://www.tennessee.gov/tccy/tnchild/36/36-2-318.htm)

Birth Father-Putative Father Registry-Birth Father (http://adoption.about.com/od/adoptionrights/p/tennesseefather.htm)