The Palladium Fantasy RPG, and by extension Rifts, allow player characters such as dragons with no conversion or alterations necessary.
A necessary supplement for such an endeavour using the 2nd Edition of the rules includes the Dragons and Gods book, which has a section dealing with playing dragons specifically. The book has notes on culture, maturation, drives, a deeper look into their natural abilities, experience charts, and all the species in one volume.
The first edition of the rules can be found as a pdf download from DrivethruRPG. If opting to use this edition of the rules, dragons can be found in the core book, with full stat and ability ranges for generation, but less overall social/cultural information, making the Dragons and Gods book fairly useful for both approaches.