I am not in the rental business but I will be happy to send to you what is in the mls. Here are 3 great rental companies in Charlotte. You should also go on the cms website and look at the boundaries for the school. The apartment complexes in the boundaries should go to Prov. Spring. I attached a link to the map.
Call me at 704-491-8026. I am a Realtor in Charlotte and live in the area you want to relocate to. I also have very strong relationships with some of the property managers of the apartment communities within the Providence Springs Elementary area and can put you in touch directly with them.
Dwell in the possibilities,
That is a tough question... since I don't know a lot of apartment complexes. But you need to find one that is To the West of McKee and Tilley Morris Road and to the North of Providence Road and South of Weddington Road. It looks like the school boundary line goes thru Providence Plantation so I don't think there are any apartments on the North West side of that school district. If you go out Providence Road and turn Left on McKee Road, any apartments to your left should be in that school district.
Once you get a potential address go to this website and zoom in on it and you can see the assigned schools. http://maps.co.mecklenburg.nc.us/geoportal/ I think you may have very limited choices to pick from to get into that school. I actually think you have found a flaw in the school system!