Hi Rebecca: other than another skylight, you can close it up, but that will involve putting up wood, wallboard and shingles :( Lots of work. You can always put a stained glass type piece of glass there and let the sun shine through that, or put up some sort of iron work and hang plants from it :)
Here are some sites that address removing them:
If this is inside your house, your best bet is to hire a contractor to seal this up properly or install another skylight. So many things can go wrong presently and in the future, it is money well spent to do it right.
You can patch the sheet rock or make it a focal point by putting a medallion or a framed panel of wood or pressed tin.
Hi Rebecca, maybe you could replace the skylight with a high R value custom window with a tint on it. Or have a pro come in to repair the hole left by the old skylight. I did find this video, I hope it helps you out.
I’m assuming you’ve closed it in and shingled over the hole? What is your ceiling material?
Hi! Here's a great video:
You can frame it in and add lighting with a decorative cover that could lift up to replace bulbs when needed. Could be very creative.
Did you patch the hole in the roof and replace shingles? For the inside I would frame it out and patch with drywall. Another option is install led lights in the chase for extra lighting
If you haven't done anything to stop the weather, I would call in a Builder or Roofer to finish the job, before the weather turns.
Is there a reason why you took out the skylight to begin with? Is it worth replacing with another one? Otherwise, just close it up with some sheetrock and paint it to match the rest of the ceiling.
Hope this info helps you out