In the 1800s, not everyone could afford a gravestone and the majority of the population were buried without one. However I see that Andrew was a Police Pensioner, so he ought to have been a bit better off and was therefore more likely to have one. He died in Unagh which is in the parish of Lissan. Worth checking graveyards in that parish as well as Cookstown (which is in Derryloran).
Not all graveyards have their gravestones on-line and there is often no alternative but to going round them in person.
I looked in the papers to see if there were funeral notices for Andrew and his wife, as those often mention where the burial is to take place, but I cannot see any for this couple.