To my knowledge most car services don't offer child seats. They're not legally required for livery vehicles or taxis in New York. Not sure about the rules in New Jersey (where EWR is).

One car service I know for sure offers child seats is Eastern:

http://www.easterncarservice.com/airport_rates.php

Their rates are competitive with the cheaper services. They charge $5 extra for a child seat and maybe $10 or $20 extra for a minivan that will hold your whole crew. I've only used them for rides to the airport, not rides from the airport, but they say on their rates page that they give a 45 minute grace period for international arrivals (and waiting time is only $35/hr after that).