"To rain" is to "rainy", as "to ..." is to "sunny"?
Some days I awake to rain.
Other days I awake to shine.
Rain or shine, sunny or rainy, I awake.
I am not aware of an unambiguously clear verb for this situation. Of your three suggestions "sunshining" is the only one which would portray meaning, but it is not a real verb. There are, however, expression which portray an action for this kind of whether, such as "The sun is shining outside" or even perhaps "It is shining brightly," but "It is shining" does not unambiguously relate to weather like "to rain" and "to snow" do.