I keep reading that people have trouble with tires on a trainer. I do not understand why.
Here is what I do with zero problems:
Use 700 x 28 Continentals at 17 to 20 MPH every day for at least one hour and have done six hours/day.
Use 700 x 38 Bontragers at 16 to 18 MPH if the above bike is used on the road.
I use very low preload of the resistance roller to tire, just enough so it does not slip. I have done this for about two years. BTW, CycleOps Fl 2.