I found what appears to be a match at familysearch.org under Texas Death Records.It is John Williamson, born 30 Aug 1839 in New Orleans, LA and died 8 Oct 1912 in Galveston, Galveston Co., TX.His parents are listed as Richard Williamson and Mary Seralis, both born in Yorkshire, ENG.He is listed as being buried in Lake View Cem.
In the same records, Mary is shown as being born 15 Oct 1849 in Germany, died 22 Jan 1937 in Galveston, Galveston Co., TX, and buried at Lakeview Cem.She is listed as being widowed and was married to John Williamson.Her father is listed as Peter Urb (spelling can be interesting when things are done phonetically), born in Germany.
In the 1880 Census for Galveston, there is a I. Williamson, 40, b. LA who is a policeman (handwritten J and I look similar and the form of the 1880 Census that I have is transcribed) that would seem to match your family.His wife is M. Williamson, 30, b. Germany.They have sons R. who is 12 and I. (again handwriting) who is 10 and daughters E. who is 7, Nora who is 5, and Mary who is 2.
I am not related (my Williamsons were in Tennessee, but know where to find some of these resources.