Hi Pat, This is all the information I have so far.I, too, am researching the Burnes, along with the Wallers, as my children are Wallers, and have been told since I was married to their father, that they are part Indian.We are now tracing that heritage. Listed below is all I have so far on the Burnes/Cherokee connection.
Taylor Burnes came to the US from Ireland about 1830. He and his wife, unknown as yet, settled in Atlanta,Ga. area.They had 3 sons, Taylor II, Thomas Jefferson, and John.They also had 2 daughters, names unknown.
The second son, Thomas Jefferson, was born on 20 Mar 1843, on a farm outside of Atlanta, GA. He was married to Nancy Jane Mabry about 1868. Nancy Jane Mabry was born in Mississippi on 31 May 1847.She was the daughter of John Mabry, a Cherokee Indian.She had 2 brothers, Jim and Bob Mabry.
T.J.(Thomas Jefferson) and Nancy had 15 children, 11 of which lived to adulthood. These were: IKE, MELLISSA, FANNY (who married my husbands grandfather), ROSIE, THOMAS ALFRED, TAYLOR, JOHN, ED, DAN, BOB and DOC.
T.J. was in the Oklahoma Landrush, 22 April 1889.They homesteaded 40 acres of land around Marlow and Dixie, Oklahoma.
Nancy died in 1924 at the age of 75, and T.J. died in 1939 at the age of 96.They are both buried in Dixie Cemetery, Stephens County, Oklahoma.
Hope this is helpful, and if I can be of any other help, please let me know.Meanwhile, if you come across anything on the Wallers while you are doing your research, please let me know.