I was able to find two counties in Georgia that I think may fit the description of what the OP is looking for.
Baldwin County
Population (2010): 45,720
County Seat: Milledgeville
Demographics (2010)
54.03% Non-Hispanic White
41.26% Black
2.01% Hispanic
1.27% Asian
1.08% Multiracial
Election Results
1992: D+ 13.15
1996: D+ 10.44
2000: R+ 1.22
2004: R+ 6.41
2008: D+ 4.61
2012: D+ 5.50
2016: D+ 1.69
Liberty County
Population (2010): 63,453
County Seat: Hinesville
Demographics (2010)
42.69% Non-Hispanic White
41.00% Black
9.71% Hispanic
3.49% Multiracial
1.86% Asian
Election Results
1992: D+ 12.93
1996: D+ 17.47
2000: D+ 8.94
2004: D+ 3.81
2008: D+ 28.33
2012: D+ 30.21
2016: D+ 21.20
Again, not sure if Liberty County would be considered "rural" to some, so make what you will of it.
Liberty County sounds pretty close. Still, 41% Black means that White voters must have preferred Trump by a large margin. Even so, a relatively small Southern county where Clinton reached well into the 30s among white voters seems like quite an achievement. Thank you all!