These Coffmans are something else aren't they?I would recommend a couple of places to look for your Wm. H. prior to 1870.Many of them were in Limestone Co., AL from ca 1830.Prior to AL they were in Jefferson and Grainger Counties, TN.There were numerous Wm.'s so I can't swear that your Wm. is there.
My husband's grandmother was also born in Hardin Co. but in 1904.Her grandfather was James Ceberry Coffman and right now it looks as if he was probably the son of Coleman Henderson Coffman.Coleman was the son of David Harmon Coffman, Jr. who died in Lauderdale Co., AL in 1869.And naturally, David Harmon, Jr.'s father was David Harmon, Sr. who was born in PA but died in 1835 in Limestone Co., AL.If you can make a connection with any of these folks, the LDS has some fairly good info to help you go further back, but you should check for other records to substantiate their files.
The Coffmans were a preacher family.I know that they are listed in some of the early TN church records.Several of the earlier Coffmans were either Primitive Baptist or Missionary Baptist preachers and the other family members were big participators in the church.