Is the Cox service your only possible source of a phone line? That is, does your apartment also have a regular phone line already installed?
If the cable service is your only means of having a phone line, you may want to call your state’s public utilities commission. They generally don’t like it when people lose their telephone lines at the whim of a painter.
I imagine the whole building got wired at the same time by the cable company, at the permission/request/expense of the property owner/manager. (My building is wired for both RCN and Comcast, and AT&T phone lines) The wiring, however stupidly it was done, was OK by the management at the time, or it would have been done differently. Therefore, it’s their issue and they need to deal with it without penalizing the tenant.
The only exception I can think of is if the OP’s unit is separately wired for a service exclusive to that unit, done by a previous tenant who then likely paid damages, but I would think it would still need to be stipulated as such (lessee’s responsibility) in the lease.
I think it is one of those annoying situations where you have to pay even though it doesn’t seem fair. Unfortunately there seem to be an increasing amount of these situations as life progresses 
You signed a lease that has internet and phone connection available.
If they take that away from you they are breaking the terms of the lease.
It’s non negotiable. At least it is here in Texas.
I suspect you did not pay for a cable installation when you moved into your rental. A previous tenant likely paid for the, now considered incorrect, installation of service.
The painters require it be removed. If you still want cable, it seems to me, you’ll have to pay up to get it. Just like everybody else moving into a place not previously wired.
It’s a drag for sure. But that’s the cost of required upgrades, ( painting the building and rewiring the cable, as required!) Like having any kind of upgrade forced upon you, always disagreeable and ill timed, but often necessary.
From time to time, things need to be upgraded. It may suck, but if it’s required, you gotta suck it up sunshine, regardless. And it’s usually the ‘user’ who pays.
Unless your lease specifies ‘cable ready’, I really don’t see that you have any reason to expect someone else should cover these costs. And it’s only $60, pretty reasonable really.
My vote is no, you alone are responsible for covering theses costs, if you want cable.
I have a friend who works maintenance for an Apartment company. Sometimes people will leave ceiling fans that they (the renter) had installed in the apartment while living there.
He told me he’s obligated to take them out even if they are nice fans and would probably help sell the apartment. The reason being, if they lease the apartment as is, and the fan breaks, the apartment complex is now responsible for replacing the fan. Even though the rest of their units don’t have one.
Here’s what I would do…I would call the landlord and say “I just talked to Cox and they need you to call and arrange for the wire to be moved since it’s on the outside of the building and not my wire” and see where that goes.
The next thing I might do is wait for the painters to actually cut the wire, then call Cox and say “Hi, my Cable just went out”. They’ll send someone to fix it and if you’re lucky, they’ll just bill the painters who decided it was a better idea to cut a wire (or the landlord who told them to do that) rather then just paint under and over the wire.
The other thing you can do, as others have said, is just to look at your lease, assuming it says you’ll be provided with cable is to go to your landlord and tell them it’s $60* and ask them how they want to handle that.
*Tell them exactly what they said on the phone WRT the price. You said “usually” $60, which sounds like the cost of a ‘truck roll’ in your area. If at all possible, I would just go with my first suggestion of getting your landlord to make the call because it’s ‘their building/their wire’.
I am not Judge Judy, but I think she would rule in your favor in small claims court.
You were provided with a service (cable) for three years, and then without cause (on your part) this service was removed. It seems fairly cut and dry that this was not YOUR fault and the management should have to pay to have it restored.
So, although I think you would win the $60 easily in small claims court, the question is would it be worth getting the $60 and pissing off your management company?
I believe the landlord already said what they would do if the ball is left in their court; cut the cable.
I’m suprised they don’t just paint over the cable. It’s not going to hurt it and it’s not going anywhere. It’ll probably look better blended into the color of the building. And in the future if it’s no longer needed you just leave it where it is.
I started off pretty strongly in the “you should pay for it” camp but have now totally switched my mind. If the cable was there before you moved in, then I think it’s the landlord’s responsibility… UNLESS there’s something specific in your lease.
Call the cableco and ask for the retention dept. Explain the situation to them and tell them that unless this “cable moving” fee is waved you will be dropping their service.
I hypothetically work for a cable company (not the one mentioned in the OP). Having (hypothetically) had experience in the customer service side here’s what I would do:
Call Cox, very nicely and pleasantly explain the situation to the rep you talk to and ask if there’s any way the fee can be waived… 99% sure they would waive it for you (although they may have to run it by a supervisor).
Keep in mind though that you WILL see the charge on your bill, along with a credit for the same amount. For reasons that I’m too lazy type out, the charge has to go on the work order so the tech gets paid for the work he’s doing.
You don’t own the outside of the building or the roof, so I’m mystified why you’d be responsible for coordinating the movement of the wire. I agree that if cable was provided as part of your rent, then the landlord is responsible for any charges related to the wiring.
Update: The manger said I’d have to pay if there was a bill…but thankfully there was no bill. The techs that came out said anything that has to do with the OUTSIDE of the apartment the customer does not have to pay for.
So, a nice relief.
I guess the woman I had on the phone either misunderstood what I needed or the thing that I needed wasn’t a complete reinstallment after all.
In other news: My lease is up here soon and I was already thinking of moving to another apartment. I think the whole “Having me pay the bill if there was one” notion has made my mind up for me to more-than-likely move.
Anyway, thank you all for giving helpful advice and suggestions.
Good on you Idle. Your landlord sounds like a real piece of work.
Thanks for the update. Glad it was good news.
30 years ago cable was wired into the attic and then inside walls in a professional manner. It was expected. Now the installers are under the gun to do considerably more installations per day which can only be done by routing the wire around the house and drilling into the outer wall of every room connected. I’ve rewired a number of them for homeowners disgusted with the shoddy work. With all the competition in the communication business it’s a simple matter of money available to do things right. It’s not there.
I would expect the landlord to pay for any alterations made to the existing wiring.
This strategy doesn’t work. Landlord will just let the tenant move out, or maybe even evict the tenant, just for being a PITA. Then landlord will get the wiring fixed and find a new tenant.
Now: I see this is in Arizona. No idea what the laws are like there. No idea if they even have any laws in Arizona. In California, a landlord is responsible to have a working phone line with ONE phone jack in every rental unit. If this wire is the ONLY source of phone service in the unit, then in California the landlord would be responsible.
Nice relief for you maybe, but we Dopers who have been diligently following this thread are thoroughly disappointed! 
Here we all were, just itching to see you & them fight, getting all excited to see the knock-down blow-out battle royale, and then, and then, … It fizzles. This is like seeing that prize fight called on account of rain. I was even selling tickets, and now I guess I have to refund them all. 