A newborn boob beanie shouldn't take more than an hour to make. I've never made one of them, but could easily. The problem is that I don't have the right colored yarn (I'm not sure how--I have yarn stashed all over the house), and I'm in the middle of another project that I'm rushing to finish by Christmas.
There's a CSO crafters Facebook group, although it might be private. If you search on this forum for crochet bear or elephant you'll find a thread where a bunch of us shared crochet projects. One of those people might be able to help. ETA: here:
http://www.car-seat.org/showthread.php?t=264288&highlight=bear
Also...I think going the CSO route would give you better results than finding a stranger at this point. I'd never do a custom order for $10. Between the price of the yarn, buying a pattern (though I could figure that one out on my own), the time it takes to make, and shipping it, I'd likely be out money. I'd do it for a friend for that price (or free), and maybe you could find someone who whipped up a bunch at once and is selling them cheap, but handmade things are often undervalued. Sorry! Like I said, if I had the yarn I'd make one for you, but I'm pretty sure I don't.