Then you might want to watch it. This is a question you might want to ask your director. They will always lead you in the right direction and will give you some things they might want to hear in your audition. Just ask your director for some ideas.
Oh. Then I have no suggestions. I saw the movie once and didn't pay any attention to it. Sorry. But you really do need to watch the movie so you can get the feel of that character so you can find the right monolouge.
Well Ryan is this (probably gay and just doesn't know it yet) flamboyant type of guy who always trails in his sisters shadow. So you'll want one that covers his lack of ability to take the lead, his excessive "spirit finger like personality" etc etc, mainly I think the best you can do is just have a lot of fun with the character. You could probably take most any comic monologue and twist it how you want. I can't think of a monologue right now (too darn early in the morning!) but I'll let ya know if I do. And good luck watching the movie I couldn't stand it =P
HSM- it looks like someone took a shit on Footloose.
No idea about monologues, but just to add to what singinsilly said, I'm in the musical right now, and Ryan wants to get out of Sharpay's shadow a lot more than in the movie (once you've seen that). There's actually a bit of character development for the two in the musical. For instance, in the end Ryan chooses to defy Sharpay and tells Ms. Darbus that they abused their power as leaders of the drama club.
Sorry, this probably isn't much help. It's actually funny to me that singinsilly said he's "probably gay and just doesn't know it yet" because our actor playing Ryan is gay, and is constantly turning Ryan's innocent lines into horrible innuendo. "Ready for the BIG GAME, Troy?"
Of course whenever he does it, our director starts shouting that "this is Disney!" and then Ryan just says the line in the most excited "Disney" way possible.