I believe this to be the location of the cemetery as Mr John Allen says it is about 300 yards southwest of the old barn on a knoll in the middle of a field. Further he says that travel down a slope and back up to the cemetery. On the above maps there is a knoll and the three lined thicket is about in the center of the hill top. Of course they are in the process of clearing the trees so in the future one should be able to spot the stone with this kind of map. It is at: Latitude: N 35.65168  X  Longitude: W -87.22971.
There are maps out there such as Delorme and MS Streets & Trips that have this coordinates on it and that is the reason I never found this cemetery when researching this area of the Maury County:  N 35.65618  X  W Longitude: W -87.23584. These are wrong so do not go there.

This map shows the big picture of all the roads needed to get to the Cooke cemetery. From Williamsport, take Cross Bridges Rd. and go 1 & 1/2 miles. Turn left on Jimmy Gray Robinson Road. After about 1 mile go into the private drive about 500 yards east of the bend in the road back north. The residential road is on your left and the cemetery will be down a field road southwest of the home. Go by the home on the west side and continue on the field road on the west side of two barns and after you pass the really old barn go another 300 yards toward the southwest to a knoll and the cemetery is on that knoll. 4109 Jimmy Gray Robinson is not the exact address as this mapped as approximate.
These are the instructions given by Mr. Fred Lee Hawkins in 1988: From Williamsport, take Cross Bridges Rd. and go three miles. The cemetery is south of road on old Leonard Johnson place. It is on a small knoll beyond barns in a field covered with broom sage and bushes.  

I can't be absolutely certain of the location therefore (yellow pointer) I will not be correcting this with the GNIS until I get a first hand account proven, but I am convinced this is at least very close. [CWA 30 Nov 2012]