Honey to me. Darlin’ doesn’t sound right at all.
MEtv has morning cartoons, a mix of Loonie Tunes, Tom and Jerry and Popeye and the Bugs Bunny show on Saturday mornings.
I find Gossamer quite INNNNteresting. I mean, monsters are the most INNNteresting people. The places they must go, the people they must see - they must lead INNNteresting lives.
Definitely “honey”. In seventh grade for the school music night my class sang “Roaring 20s” style songs including this one. I also have “Yes, We Have no Bananas”, “Yes Sir, That’s My Baby” and “My Blue Heaven” as recurring earworms nearly 50 years later…
And you would know, having worked on the inside. Did you ever meet MJ Frog whilst trying to blow up the world?
Of course I did. We worked together in 1995:
I thought of “darlin’” as well even thought I saw the frog cartoon many times. But now that you mention the alternate ending to Big, I’m sure that’s where I remember darlin’. 
I was pretty sure it was Honey. As to the origins of “darling,” I’d wager a guess that “Oh my darling, oh my darling, oh my darling, Clementine” might have something to do with it. You have “o my darling” in Clementine, and “[Hell]o my darling” in the incorrect version of the Ragtime Gal song.
Sort of like “All around the mulberry bush, the monkey chased the weasel”?
Honey, and I know it because of the singing frog.
Ditto. I haven’t seen the sheet music (not in a while, anyway), but “Honey” is sung as two very short syllables in the cartoon. “Darling” just wouldn’t fit rhythmically.
Huh? It fits just fine. Same amount of syllables, same stress pattern. About a third of the respondents seem to have it naturally fit there without a problem, and I have no issue with hearing it either as “honey” or “darlin(g)”
I just also realised I remember the last line as “telephone and tell me I’m your guy.” I’m not even a guy.
“…I’m your own.”
Totally cromulent also.
I think, in the Chordettes’ version of it, they sing, “telephone and tell my you’re my own.”
You’re right, I just watched the cartoon again (possibly first time this century) and my recollection of the rhythm was incorrect.
I didn’t know : “Hello” was a relatively new word at the end of the 19th century, and was closely associated with the telephone. So this was a sort of steampunk romance song.
ETA : Should have read the song’s Wiki entry.
“Ahoy, hoy, my baby,”? I 'unno.
But consider,
Hello my baby
Hello my honey
as opposed to
Hello my baby
Hello my darlin’
To my ear the “bee - ney” at the ends sounds more like tin pan alley than “bee - lin.”
See, when I remember the song I remember it as hello my BA-by, not ba-BY. Watching the video tells me you’re right, the frog sings it ba-BY, but in my head that’s not how it goes, probably because that’s not the way you usually pronounce baby.