An interesting and insightful article from First Things about public prayer by Christians for events not strictly Christian. I'm 99.99% in agreement, I think, but the conclusion is one that I have difficulty endorsing wholeheartedly.
When I was much younger, surely no more than 17, I was asked to give an opening prayer at an event of which I was a participant. Without getting into details about the event, when I asked what sort of prayer was expected of me and received the reply that it was to be general and ecumenical, I noted that I would not be willing to alter the way I prayed and would invoke the name of Jesus. After a bit of surprise on the part of the person asking me, he withdrew the offer to have me pray. Frankly, at the time, I felt more relief than anything. Not only was I nervous about how my prayer would have been received had I held to my convictions, but I was very nervous about praying in front of several hundred people.