This is obviously an old forum. I see though, the cyberhymnal website still has some other tune called "Resignation" and so the question is still not resolved. I hope the following is helpful:

In The Baptist Hymnal (1973 The Baptist Federation of Canada) at number 447 has the tune listed as C.M.D., 3/4 in D from J. Funk's "Genuine Church Music" 1832. The lyrics are "My Shepherd will Supply my Need." The United Church of Canada book, "Voices United" (1996) features two other sets of lyrics. At numbers 494 it is 3/4 in C, 7.6.7.6.D and 780 is 6/4 in C, 8.6.8.6.D. Music source is William Walker's Southern Harmony 1835.

I recognised the tune during the opening scenes of the TV movie, The Day After (1983) a story about the devastation of nuclear holocaust in a small American town.

Hope that helps anyone still trying to find the answer.