Hello Bethan
On familysearch.org, I found this family that could be yours.
John R Davies, age 37, born -- Wales
Clara Davies, age 24 , born -- PA
Harry Reed Davies, age 6, born PA
Clara L Davies , age 4 , born IL
Source Information
Census Place --Little Rock, Pulaski, Arkansas
Family History Library Film 1254054
NA Film Number T9-0054
Page Number 322B
The family information was from the 1880 United States census. If I remember right, I seen a John R Davies birth or christening in 1843. I will try to retrace my search and maybe able to get back to you.
Bob