This works for me. I can copy-paste a Sprite from one instance of Construct 2 to another. (It also works if you open two projects in one instance of Construct 2.) What is it you're trying exactly?
I made my game for the Windows 8 competition by using the Template:Auto Runner and after I got it working the way I want I decided to copy and paste the items needed for Windows 8 games(Share button, Purchase button, etc...) from the Windows 8 template.
I just did this with my game. I wanted to test out a specific part of my events and wanted to copy that part of my game to another project for tests.
To copy objects, you have to copy the sprite on the Layout window, and paste it onto the 2nd layout window.
Ah! Thank you, there is my problem. I was trying to copy(Ctrl+C) items from the directory tree in the Projects panel of the first instance and pasting(Ctrl+V) into the Projects panel of the second instance.
Copy and pasting from the layout worked, I should have figured that out myself, but thanks to everyone who helped!