I've got an arduino controlling a small stepper through a ULN2803. Works fine for just playing around.
I was looking at driving a larger stepper and thought about using TIP122. Now if I know the max current per coil of the stepper, and that value does not exceed the capabilities of the TIP122 then would this approach work?
You should be OK. Just limit the current going into the transistor with a 1k resistor and make sure you have a freewheel diode across the load (the ULN parts has these integrated). not sure what your electronics knowledge is like, but have a look at the following link: https://www.jaycar.com.au/images_uploaded/relaydrv.pdf