Do any Catholic Colleges offer PhD programs?
Dozens do. If you are serious about a Ph.D. program you should spend time talking about them with a faculty mentor in your undergraduate institution. Doctoral studies are time consuming, money consuming (even with a fellowship), and will change your life in ways you can’t possibly predict. You will need to go into one armed with all information possible, and you will soon find that even that isn’t enough.
Do any offer scholarships or fellowships for Catholics?
Any Ph.D. program worth considering will fully fund its students. If a program doesn’t fully fund you DO NOT GO. Unless you are personally wealthy, you can’t break this rule.
On the same hand, no program worth considering will take your religion into account regarding funding. If a program even asks you about your religion, you should look into another institution. Ph.D.'s (regardless of the discipline) are not about creed, but about following evidentiary lines through research.
I would be interested in finding out since I am a Catholic who is thinking about getting a PhD.
I, and probably many others here, would be happy to help. You need to start by determining your discipline. No advice more specific than I have given here is useful without your discipline.
You can take a look at the forums for the Chronicle of Higher Education for some more information. They can be found at
www.chronicle.com.
A Ph.D. program is both the most exciting time of an academic career, and the most brutally demoralizing. You live with both extremes for all 4, 5, 6, 7, 8… years.