Out of curiously, is this for 1st cousins? In other words, does the person you are doing this for have any living 1st cousins? Just to be clear, children of your great uncle's brothers or sisters. This wasn't clear from the OP.
I did some reading and that is really the furthest they will go. I found a couple of sites online that do cousin testing where they offer a 3 person tests. I assume it is more accurate if there is DNA from more than 2 people.
I have a feeling if that can't be managed then you're looking at digging people up.