I couldn’t find much and possibly you already have what I did find.

Peter Cullen married Cynthia Handy 8 Mar 1875 in Lafayette Co. AR. (see attachment below)

1880 Lafayette Co. AR
Self Peter Cullen M 26 Arkansas
Wife Cinthia Cullen F 25 Arkansas
Daughter Sussie Cullen F 2 Arkansas

1900 Lafayette Co. AR
Head Peter Cullen M 48 Arkansas
Wife Lucinda Cullen F 44 Arkansas
Son Charlie Cullen M 12 Arkansas
Daughter Edna Cullen F 10 Arkansas
Boarder Lillie Bridges F 17 Arkansas

I couldn't find anything after 1900. Good luck