Diamond- April's birthstone is the diamond. Unfortunately, she sounds a little dated (and some would say unsophisticated). I'd try something related to diamonds. Clarity, perhaps?
Daisy- Daisy is an adorable name. She's #198 in popularity, and can be used on her own, or as a nickname for Margaret or Marguerite.
Sweet Pea- Sweet Pea is more of a term of endearment than a given name. But, using a P name makes the title more appropriate. Pick a "sweet P name" like Posy, Poppy, or Penelope.
Red- There's a plethora of red names, but if you're looking for something unusual, I like Carmine, Crimson, and Russet.
Yellow- My favorite yellow-hued name is Citrine--so bright and cheerful! Jasmine, Saffron, and Amber are some other nice options.
Aries- Aries has potential as a stand-alone name, but he (or she) might not work in all cases. Arie works well and has a similar sound.
Taurus- Taurus is my favorite zodiac name. He's cool, strong, and very unique. Taurus would make an especially daring middle.
Related to April:
April Names- April herself is an obvious choice for this month, but she's a bit dated for the month names. Avril and Abril (French and Spanish, respectively) could be fresher options.
Arbor Day- Arbor Day is the last Friday of April. If your babe is born around this time, it's definitely worth considering a tree name. Elm, Linden, Oak, Willow, and Pine are just a few of the options available. Arbor would make a cool name as well!
Earth Day- Earth Day is the 22nd. Along with the Arbor Day tree names, you could use Eartha, Tierra, Sky, or any other natural name.
Easter- If you're having an Easter baby, why not consider a name tie-in like Pascal, Pascoe, Palma, Calla, or even Easter herself.