I was reviewing my Derby info and found the following which may interest you.
In the 1st and 2nd valuation of tenements (1859-75) there was recorded a Robert Derby of Derrygarve, near Castledawson, who rented a house from a Thomas Derby. This was until around 1871 when there was a new occupier. My great grandfather, Suffern Garvin,(husband of Sarah Derby) later aquired these houses and land. This could be your breakthrough but I dont know how you would get more information to prove it was the same Robert.