Possibility of getting a UID on Arduino
You could use a small silicon serial chip like the Maxim DS2401 (http://pdfserv.maximintegrated.com/en/ds/DS2401.pdf)

An other method is to use good old dipswitches. That way you set each of your 'transmitter' to different address using the dipswitch. On boot the Arduino reads the switches to know it's address and uses that.