I have never had triplets in a game before. Today luckily my Flowers family had three new baby girls, Pansy, Daisy, and Poppy.
This is how I did it:
Step 1 - Both parents (young adults) had fertility treatments
Step 2 - Romance
Step 3 - Didn't eat any watermelons, or apples
Step 4 - I put stereos and TVs set to kids channels in every room the mom sat in
Step 5 - Had mom read both baby books in the rooms with the stereos and TVs on kids channels
Step 6 - Had mom relax, and dad do everything, especially the stinky jobs
Step 7 - Waited four Sims days,
and got her to the hospital as fast as as the taxi could go! The Flower triplets:
The Flower triplets' room: