No there aren't any specific key code for Done/OK/Next key. For simulating those we need to send the metastate along with the keycode of "Enter" key.
driver.sendKeyEvent(key, metastate);
For sending the Next/Done key metastate code is 16.
If that not working we can send the KEYCODE_DPAD_DOWN (for Next).
And these are just workaround if the thing are not working as expected.