If sunshine is significantly depleting chlorine in the pool, then you might want to raise CYA. BTW, what is your CYA level?

It doesn't really matter if you run at night or during the day if the FC level at it's minimum is sufficient for the given CYA level. If you run at night, you may need to bring the level up higher so it lasts all day while the pump is off. However, if you run during the day, then chlorine will be added as the sun degrades it so the "peak" chlorine level may not need to be as high.