This is an example of a "single cut SQUINT". To create this look, plunge the knife tip into the wood twice to create this angled cut. This squinty eye, along with some round puffy cheeks, makes for happy look.
This example used the same two cuts as the previous example, but has a cut connecting the two. This example can be painted within the knife cuts.
Some times the face you carve is more of a cartoon character, and you need an eye that fits that face. This cartoon eye is simple enough.
Here's a straight cut plus. The plus is the line cut out over the triangle cut eye, and the bag under the eye. This is a little more towards the realistic eye.
Here's a humble example of an eye with cured and straight cuts. With an eye this small (1/4"), one must use a series of small connected stab cuts with the knife tip to make the tight/small curve cuts, or risk breaking the knife tip.
These are but a few ideas among many. If anyone wants to add another example you can do it by e mailing me at firstname.lastname@example.org, and I will add it to the list.