The Chordettes had a number of similar hits, including Lollipop, and Born To Be With You.
I kind of see them as a crossover from the jazz influence of the late 40's (Andrews Sisters, for example) to the doo-wop bands that came a bit later. Anyhow, you asked for similar era music, and although most of what I like comes from slightly later, it isnt so dissimilar.
Your post gives me the impression that you know very little about this era, so these songs are somewhat reasonably well known. My apologies to those posters who think I am re-covering old ground.