If it's the same two words, you only have to copy once. After that it's click-paste. (Use the keyboard shortcut for paste. On the Mac it's Command-V; on Windows I believe its Control-V)
Since you have to select the box anyway to tell Quark which one gets the new contents, this amounts to a one-press solution per box.
Unless you can carefully specify which boxes you want in advance, this is about as simple as it gets.
If you can either select all the appropriate boxes or specify them (say by position) AND you're on a Mac, you can write an AppleScript to fill each of them with the text in your clipboard. That would be faster and easier once you wrote the script. (Could help you with that if you're on a Mac. Nothing comparable on the Windows side, though. Sorry.)