Babiesovernight.com is an illegal website that is accessible at the TW@ Internet Café in Grand Theft Auto IV. The website is a reference to petsovernight.com" from Grand Theft Auto III, as both sites have similar names and taglines. As a minor detail, the part where the countries from Africa are listed, the one called Pambia does not exist.
As advertised on the radio, Babies Overnight is a service that you can pick out the style of baby you want (referencing that some naturally-born babies are ugly) and accessorize him and the baby will box-ship to your front door anywhere in Liberty City in a matter of hours.
It should be noticed that online baby adoption is illegal.