Broadening the definition of 'soundtrack' to 'music that appears in the movie' (since this is written into it as part of the dialogue)...
I know the movie this is taken from is very silly (not a criticism; it's been one of my favorites for as long as I can remember), but I honestly find this to be pretty sweet and endearing, especially in the context of the story:
Hmm. Well...I'm a big ol' sap!
I'm actually kind of embarrassed to admit that I didn't know until I went looking for this song to post in this thread that this is a rendition of an actual song from 1917 performed by Broadway actress and vocalist Mary Cahill:
That's
more than a little bit before my time, but totally in keeping with Steve Martin's old-timey aesthetic, as is obvious from his banjo records (which are all great).