How do I convince them this is the truth?

Okay, well I have a friend who lives in New York. She has a Facebook, Twitter, etc, so a few of my friends have noticed our friendship. This used to be no problem, but lately my friends have been thinking I 'made her up', because she only has 100 or so friends on Facebook and since she's pretty, they ume that her pictures are photoshopped. At first, I thought their accusations were rather funny, but now they are just rude and annoying. I can't go one day without them pestering me saying how she's 'fake' and how I 'made her up', but I didn't, and I told them that. How do I deal with them, or prove to them she's a real person? We don't have the money to fly her in from New York, so what should I do?