If you are truly wanting a day/night cycle, shouldn't you be setting the background color/image as well?
I'm an idiot, I just figured out you were talking about the black border. Yeah - well normally that wouldn't be visible (I am working with small maps because they're easier to debug etc & my map editor isn't exactly the most stable thing in the world.The way I do it for anyone interested:
What happens is the ambient colour is layered over the screen (day\night shade) - the point-light sources have an area they're going to apply their lighting effect too as well and I can't cover those areas (otherwise I lose significant quality with my lighting.) So I use two Area objects, one covers the entire area of my map, the other I add my light source's effect area to - then I subtract my light source area from my world map area and draw the ambient light using the world map area.
Then I fill in the spaces I didn't apply the overlay to with the lighting effects by calling the respective pointlight's rendering routine (which is passed an ambient colour to lerp with).
This system allows me to implement all sorts of lights too (like, i.e directional lights)