Most likely a no-no, but I have read about someone where mixing the species worked for a while, before a coturnix turned on a button. The sex of the birds might play a role - I think two females have the best chances. If the 'habitat' is very large, that probably increases the chances as well. But if you have other options at all, I'd not attempt it.
Buttons can die from stress if they are kept alone, so I'd definitely get another button. I don't think coturnix are as prone to that, but I'd still not keep it alone. If it's female, a single female friend is enough - but make sure to do the introductions slowly, they can be very aggressive towards new birds. If it's male, a male friend might work as long as there are no females around - otherwise 4-7 female friends.
