Much depends on what was agreed to at purchase, how the agreement was documented, and whether you have since agreed to modify the agreement.
In Arizona, if there is no written lease, the court treats the occupancy as a month to month tenancy, so either party can terminate it by giving at least 30 days written notice to the other. You can file a forcible detainer lawsuit (an eviction) after the appropriate time has passed.
It sounds like you were on pretty good terms with the co-signor when you needed her help to get the loan: though the law doesn't require it, I suggest that you try to work together to chose a move out date you both agee to, rather than give her a unliateral demand. If you reach an agreement, you should put it down on paper (or, preferably, schedule a meeting with a lawyer who can help spot problems you have overlooked, like what language is required to terminate the month to month tenancy, whether any "equitable" interest in the property needs to be addressed, etc.)