Is it possible to send text messages from a payphone?

Bell Canada equips a portion of its payphones with QWERTY keyboards that are used to send SMS text messages:
Bell Canada Payphone QWERTY Keyboard.

In Australia Telstra has equipped all its payphones with text message capability:
http://www.telstra.com.au/abouttelstra/c…

I don’t know of any payphones in the United States specifically equipped to send SMS, unless there is a way to do it through a payphone TTY/TDD/VCO device.

For a number of years the TCC Teleplex company had a dozen or so hybrid payphones in New York. Though they did not specifically advertise that you could send text messages one could presumably have accomplished that via e-mail or a web interface:
TCC Teleplex Payphone Internet Kiosk.

Earlier hybrid payphones which allowed for e-mail and web (and presumably SMS via those gateways) could be found at major airports. The most popular such phone was the AT&T Public Phone 2000.:
AT&T Public Phone 2000.