Let me just start off by saying, "I LOVE THESE!!!" I am turning our homemade Angry Super Bird costumes into pillows. Are you looking for ideas for Christmas? I am planning on making some Star Wars themed one for my kids for Christmas.
You can follow the tutorial here to make normal Angry Birds costumes. If you are going to make the pillows, you do not need to use the muslin. You can just do the felt.
You can make any character you want. I found this link to a page with characters cartoonified in circles- which would make it easier for you to make a round pillow looking like your child's favorite character.
Start off with felt- approximately .5 to .75 yards, depending how big you want to make it. You need to cut two circles of your main felt. To make a circle, fold the felt in half, then in half again. On the corner between the two sides with folds, place a piece of yarn, then stretch it out along the edge of the felt. While holding the yarn stretched out, draw an arch across the felt to the other side by moving the yarn like a pendulum and keeping the marker at the far end of the yarn. Cut along this line, open it up and you will have a circle. Cut out one more. For this Super Mario pillow, I used a 13 inch piece of yarn, so the circle ends up being 26 inches wide.
Sew the front to the back of the pillow- the design should be on the inside. Leave a six to eight inch wide opening so you can invert the pillow and then stuff it.