Your tenant cannot pull a contract out of thin air, you had no agreement with her to provide a cell phone so that's her problem.
Secondly, frequently what we perceive as problems on the land line are often problems with the handset. We provide a land line in each of our rentals, but it is up to the tenant to provide their own handset. If the telephone company said their line was clear or repaired and the problem persisted, more than likely it was her handset that was at fault. Sounds more like she wanted a cell phone and now wants someone else to pay for it. If she wants she can take you to small claims court but she has the burden of proof.