Although I installed all Coptic fonts, it still wouldn't display correctly in Google Chrome, showing mostly squares, and only a few Coptic letters. However, I found a fix. Here are the steps:
1. Download and install the Code2000 unicode font here: http://home.bishoy.com.au/downloads/code2000.ttf
2. Open Google Chrome.
3. Click on the menu icon, then navigate to: Tools > Encoding > Unicode (UTF-8)
4. Turn on Auto detect in the same menu, if it is not on already.
5. Close and re-open Chrome. If necessary, restart your computer, too.
Coptic should now display correctly! I hope this helps others with my problem.