How can I convert a ventless propane fireplace to natural gas?
The short answer is all you need is a new orifice.

The complicated answer is : don't do that.  Ventless systems have been banned in various places, and come with significant hazards not fully mitigated by a carbon monoxide detector.  Read for instance : http://www.energyvanguard.com/blog-building-science-HERS-BPI/bid/48762/Bob-Vila-and-the-Vent-Free-Gas-Fireplace-A-Sorry-State-of-Affairs

A choice quote: "After doing research, we decided we would never put a vent-free (room vented) appliance into our home. Because of this decision, we didn't believe it would be right to sell them to our customers."

I would suggest asking a different question "how can I vent this ventless gas log set?".  You could also calculate the number of heating days : if this is just decoration perhaps it's cheaper to just run it on propane until it dies.