You can make a sky dome using CS, or you can use some after effects.
In RCT3, use
Dasmatze's Background Boxes and place a box around the part of the shot you want to replace. If you are using anti-aliasing, choose a color that is most opposite from the skyline. If you're not, it shouldn't matter what color you use.
After you take your screenshot, you should have a regular picture with a solid colored sky. Now use Photoshop (If you want to know how to get it, PM me), and open the picture. In the menu bar, click Select > Color Range. Then click on the color of the picture that you want as the sky, and change the fuzziness until you get the right result. Then click okay.
Now you will have a perfect selection of the sky. Unlock the background layer and then click the delete button. Then you'll have a grid behind your picture. Go on the internet and find a replacement sky that best fits your image.
Right click and copy the image and paste it into Photoshop. Move the sky layer behind the original, and save it as an image (I prefer PNG). Then you're all done!