Sayuri, Fazlin Hanim, kfif, MeegsS, cuzie, IWatchDramas, and Susiqt - Added!  Thank you!  :)

lily_b - Thanks for the rec!  I'll bump that one up on my priority list. :)

EveryGrimmRose - Thanks, but that one's already on the list.  It's actually the one that made me a fan of the "secret pregnancy/birth" theme!  :D

cuzie - Does Jumong fall more into the "single father" theme, or is the mother the female lead in the drama?

Susiqt - Thanks, but Good Job, Good Job / Wonderful Life / Loving, Never Forgetting are already on the list. ;)
Jenny & Juno both try to keep the pregnancie a secret from their parents and Dear Sister her family and the child father only discovers after some episodes
kfif - Added Dear Sister.  Thanks!  :)

Jenny & Juno I'll leave off the list, since the pregnancy isn't a secret from the father.
I have only watched the original (Taiwanese version) of Fated to Love You and everyone else saying that it's the better one so I recommend that though it wasn't really a secret pregnancy/birth lol. You may also try Sunny Happiness though the plot line you're looking for isn't the story of the female lead, she's just somewhat involved in it :) For the films, I don't think I've seen any and Present Perfect comes close to it (spoiler alert!). A really good Thai short film :)

I love this plot line as well that's why Autumn's Concerto Loving Never Forgetting are part of my fave dramas haha!

Far away love - It's a bit complicated to explain but its really good stars Park Hae Jin