There seems to be some confusion in terminology. I understand the ceiling joists to support the ceiling finish, support no live loads, and serve to tie the rafter ends together to form a triangular truss like structure. The ceiling joist size will depend on whether you will be installing knee braces and purlins or not. Such a ceiling joist you can figure a 10 psf dead load for span tables, but with knee braces, you can't use span tables. The roof dead load depends on your roofing material. For regular asphalt shingles, figure 15psf dead load, much more for tiles. The roof live load will typically be some portion of the ground snowload, depending on roofing material and pitch. Some jurisdictions specify a roof snowload that is not reducible.
Snowloads can vary drastically by small changes in location. You should inquire with your local building authority for this kind of information. For deflection limits, 1/240 the span for ceilings is OK. For rafters with no ceiling finish in the typical attic situation, you can use 1/180 span under combined dead and live loads.
Unfortunately, there is not enough information to answer your question. If I understand your ceiling joist application correctly, a 2x6 should be adequate if no knee braces are involved, but I couldn't say for sure, it's just my gut feeling.