I looked into this several years ago, so things may have changed, and my memory may not be the most reliable.
Anyone who is not within the group of legal officials (Justices of the Peace and the like) must have religious ordination and file with a county clerk to perform a marriage. Though this is bullshit in the highest order, it probably won't change anytime soon.
One alternative is to be ordained by what is more or less a mock-church. The Church of the Sub-Genius, and several others, will ordain you with a quick online form. I know of people performing marriages in Texas through this route, though many in the state throw a fit over it, and the county clerk may refuse to recognize the ordainment (which would start a whole new pain in the ass).
Depending on what your friends exactly want, there is a simple way to go about it without you having to be official in any capacity. This would basically amount to a common law marriage. If two people of the opposite sex live together and present themselves as married, then they're married. A ceremony would certainly fit the bill for presentation. This is the route that I took a while back, and it worked out quite well. We never bothered with a marriage license, official, or county clerk. We had a friend perform the duties of an official and did nothing to involve the state.
Keep in mind that the end of such a marriage can still require legal divorce (though there are ways around that).
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From the officers:
The ACA Lecture Series continues Sunday, February 4th, 12:15pm at the Austin History Center, 9th and Guadaupe. Chase Hunter will speak on "Inside Scientology 2: the Sea Org". The lecture is free and open to the public. The building opens at noon.