Are you ready? "How do you get bicycle grease out of a shirt?"
(You have to have a wetvac (shop vac or carpet steam cleaner) to do this)
Use lots of baking soda on the stain to absorb as much of the gunk as you can, vacuuming it up as much as possible without scrubbing the fibers (scrubbing only breaks the carpet down, so don't do it!)
Then go to your laundry room and get your bottle of spray and wash, (yeah, the green bottle of blue stuff you spray on your clothes to pretreat them before you put them in the washer)
Use a fair amount of that on the stain, gently working it into the stain with your fingertips.
Next pour a LOT of HOT water over the mess, and vacuum it up. Do it again. Do it again. You want to make sure you suck up as much water as possible each time, again without scrubbing the fibers. By a LOT, I mean something like 16oz for a 6"x4" area.
Make sure you get as much water up as possible when you're done, and it should be pretty clean. If that doesn't get the grease out, try Dawn Dishwashing Liquid.
By the way, the best way to get baby clothes really really clean is hot water and Cascade powder dishwasher detergent. After all, they are FOOD stains! Don't ask how I know this, but I do.
A dad in Seattle,
(who has a puppy who isn't completely house trained, and kids who have spilled plenty of stuff on our carpets, I love my Sears Shop Vac!)