Recently we bought a home that had a sun porch that was built an existing deck. The past owners insulated the walls but not the ceiling. The ceiling is cathedral. I took off the plywood to see the joist zones. They are 24 inches off center. The joists are 2x6. Therefore I can only get batting insulation of the R-value of 11 because it can only be 3.5 inches thick. Since it is a roof in Wisconsin do you have any recommendations on how I can get better R-value? I am stuck because of the 2x6 joists that he put up there. Every where else in the house are 2x8.

Thanks for your help!

Is it also a shed style roof? If so there needs to be some roof venting added.
R19 will fit in a 2 X 6 bay.
I'd bet most of your heating and cooling loss is thruough the windows, floor and doors not the roof.

You don't want to put R-19 in a 2x6 rafter, because there will not be the required 1 1/2-inch minimum air space above it for ventilation...that is, if the roof has any ventilation, which is doubtful. Is the room heated? If not, what is the point of insulating it?

If you insist on insulating it, or if it is indeed a heated space, you can screw 2x2s or 2x3s or even 2x4s to the bottom of the rafters to create more space for insulation. In Wisconsin, you probably need R-38 at least in the roof/ceiling, but the most you can probably get in the ceiling using fiberglass is R-30c, which is 8.25 inches thick. But, there is no point in insulating if the space above won't be ventilated, or if it's an unheated space.