I am not Paizo, but if I had to make a ruling:
I would say that it does not directly prevent the effects of sunlight in regards specifically to a vampire's weakness. Only if the darkness effect reduced the actual light level to darkness or below would I count it.
Unlike protective penumbra, which specifically calls out such protection for vampires, darkness only mentions light blindness or light sensitivity (which are caused by bright light, which would be reduced one step to normal by darkness).
While sunlight is normally bright, being in normal sunlight or even dim sunlight is still being in direct sunlight. Again, this is specifically about a vampire's weakness. (We aren't going into starlight being direct sunlight, we already know that isn't intended or the case.)
If there were an object or a spell that gave off dim light that counted as sunlight, a vampire in that direct light would still be affected: bright, normal, or dim makes no difference. Although in the case of a spell or magical light effect, its level would have to be higher than the darkness effect, as per usual, to bring the illumination at least to dim (the point where there's some light).
So my ruling would be that darkness only protects a vampire against direct sunlight in situations where that light is already at a dim illumination (and lowering the level by one would place the area into darkness). Higher level darkness spells or ones which lower the illumination level by two or more steps could be effective in progressively brighter circumstances.
