This does vaguely ring a bell. I did this once for a game a long time ago. You don't need to do all the funky stuff I did back then - you can achieve exactly the same result with the clipped sprite.
Draw a long gradient, representing the sky at different times of day. Top = top of sky, Bottom = horizon color. I grabbed the gradients from a properly calculated physically correct sky.
Set clip rect to 0, 0, 0.01, 1, rescale your sprite to fit once more, i.e. scale by 100, 1, 1 to get it back to the original size. You can then change the x clip rect value to sync sky to time. It looks really good if you have a good set of gradients.