Converted from crochet instructions by Jennifer Dunne
Use a bulky-weight yarn on size 10 1/2 needles. (One Peep will take about 12-14 feet of yarn, depending on how tightly you knit.) You'll need something to stuff it with (because of the small size, you can use cotton balls) and a black magic marker to make the eyes.
Edited to add:
"Add 3" means you need a net increase of 3 stitches to the right of the existing row. You can either double-knit-front-and-back (turn 1 stitch into 4), counting that last knit-in-back as the first of the knit stitches you're supposed to do for that row, or end the previous row by casting on 3 new stitches, which you then knit at the beginning of the new row.
KFB means knit-front-and-back. Knit into the front of the stitch, as usual, but don't drop the stitch off the left needle. Instead, poke the right needle through the back like you would for a twisted knit stitch and knit a second stitch.
Cast on 10.
Rows 1-3: Knit 10.
Row 4: Add 3 at beginning of row. Knit 10. 
Row 5: Add 3 at beginning of row. Knit 13. 
Row 6: KFB. K6. KFB. KFB. K6. KFB. 
Row 7: Bind off 6. K14. 
Row 8: Bind off 6. K8. 
Row 9: Bind off 8.
Your knitted work will look nothing like a Peep at this point. :-) Your final knot of the bind-off is the crown of the Peep's head. Rows 7 and 8 are the tops of the wings. With right side out (pick whichever side looks best to you and declare it the right side), join the top of the head with kitchener or other flat join, then join back of neck and tops of wings. Stuff the head, and get it looking right. Join most of the remaining Peep, leaving enough space to stuff it. Shape the Peep as you stuff. Finish the join, and bring the yarn up through the body of the Peep and out the front of its face. THIS IS IMPORTANT! Knot the yarn to make the beak. You may need to catch a stitch on the front of the face to hold the knot close enough, or double-knot to make it big enough. The beak is what makes it look like a Peep, so take your time and keep at it until it looks right. Using the black magic marker, add dots on either side of the head for eyes.
This was the first Peep I tried, in Bernat's Baby Lash, color Soft 'n Sunny, on size 10 needles. The yarn is SO soft and fuzzy, it's a dream to work with. But given the size of the Peep, it came out looking more like a walrus. I also made the mistake of trying to finish it right-side-in, then turn it inside-out to stuff, so I then had to pick out individual eyelashes that had been stuck in the seam and pull them back to the right side.
This is a 3/4 overhead view of the same Peep, so you can see the fuzziness of the yarn. (But I'm thinking this would be perfect for that bunny blanket someone mentioned a few days ago...)
This was my second Peep, in double-stranded worsted weight yarn, on size 11 needles, to really show the stitch definition. Unfortunately, that made it loose enough that you can also see the stuffing. But it looks like a Peep. And that's really all I wanted.