Deborah, There are so very few Darbison's in the USA, you might just be kin. Odds are in favor of this.
My wife's great grandfather was Dr. George Thomas Darbison. He was born 1849 in England. The family immigrated to the US about 1854. We found them in the 1860 census living in Missouri. Then they moved to Texas by 1866. From there to Oklahoma, New Mexico, and back to Oklahoma by 1910. I'd be glad to share my Darbison file with you. We have traced the line back into England 1781.