Rentals with Screened porches
In Rock Hill:
Yorktown. They stay full, so probably hard to get one.
Forest Oaks has sunrooms, might have screened porches.
You can try driving through some areas to see if there are signs in windows at:
Corner of India Hook Road and McDow Drive condos
Cross Creek in the same area. Turn on Summerwood Drive off India Hook Rd. Condos on left.
Hunt Club Villas...From I-77 exit 82-A, turn north on Celanese Rd., left onto Hunt Club Drive.
That's all I can think of.
Don't know Fort Mill rentals well.