Not including plus Carmel and Tel Aviv [666-6666 and 777-7777, respectively] I have at least ten NYC car service numbers lodged in brain. [Funny what a decade of late nights at the office and constant travel'll do to you.] I just dialled them all and asked about car seats. Here's the tally of their unequivocal "No's":
Do you have any cars with a car seat?: 12
Do you know anyone who has some?: 10
The other two said, "Nobody does that" and "No way, man, nobody does that."
There you go, nobody. Except, as it turns out, Tri-State Limousine, which charges $25 for the car seat for either an airport run or for hourly usage around town ($40/hr, 2 hr minimum).
UPDATE: Based on the variety of responses in the comments, the original, cranky tone of this post doesn't seem all that relevant anymore. Here's a list of other car services in NYC that offer car seats: