Time-lapse photography - Day to night issue

I've picked up and intervalometer recently and I'm working on time lapse photography. I'm running into issues, though, when shooting clouds and the sun begins to set. As far as I can tell, I have two options:

1. leave the camera settings alone and let it fade (quickly) to black

2. Increase the exposure time and/or aperture as the sun sets.

Neither of these options are any good. If I want to shoot into the night, option one just doesn't work. Option two results in very clear and jarring jumps in brightness, as I adjust the exposure time.

Is there any way around this?