Hi
I have found two family trees on A****Y which shows some details matching those you have given below.
First tree shows a Joseph Rumney married to Frances Milburn who was born in Middleton in Teesdale in 1790. Parents detailed as John and Ann Rumney nee Reed. This tree is a public tree.
There is another public tree showing Joseph as born abt 1792 Middleton in Tees married to Frances Milburn buried Bishops Auckland 18 10 1837 -died of Fever. This tree shows John Rumney as Father born abt 1741 M in T and marrying Ann Reed in M in T 12 11 1766. This a public tree
If you do not have access to A****Y then please let me know and I will help further.
I did find the baptism in 1790 for a Joseph Rumney in Middleton in tees on the Familysearch website submitted by a LDS member but giving no other detail.
I assume you are aware of the Co Durham transcription website
http://genuki.cs.ncl.ac.uk/Transcriptions/DUR/My advice is to check the registers for Middleton in Tees with Durham archives.
kind regards
Sue