HiHave a look at ScotlandsPeople "church registers" other churchesYours AyeBruceL
According to Diane Baptie's Registers of the Secession Churches in Scotland, there is a baptismal register of Dalkeith West United Presbyterian Church starting in 1839, but nothing else that matches your dates. PS the term 'non-conformist' is not relevant in Scotland. A non-conformist is by definition a protestant denomination which does not conform with the established Church of England. The C of E is not 'established' in Scotland so the term has no meaning in relation to religious denominations in Scotland.