Boy that is a tough one, since my kids are older I am slightly out of touch. Truthfully I have never seen a taxi with one, I guess most people bring them. You can call the taxi office and see if they are available. You also might ask Arubalisa, she is in the know!!!
I can't say that I have heard of/seen taxis with car seats in Aruba. That being said, I would suggest that you rent a car and either bring your own car seat or rent one from the car rental company while you are in Aruba. That way you would be able to come and go as you please without having to worry about arranging for transportation with a car seat.
We went w/Jet Blue from NY; and took the car seat (for grand son); here is JB's info on it; http://help.jetblue.com/SRVS/CGI-BIN...ase=obj(373795)
"... checking a child safety seat, it will not count as one of your checked bags and there is no fee assessed..." read more in da Link