We would say that it's definitely possible, but it depends on your budget and travel habits as to how best to go about this mission.
The Donny & Marie show has long been the most expensive ticet in town, so there's no such thing as a cheap seat -- the cheapest is $121, inclusive of taxes and fees. If you're willing to really push the boat out, there's a VIP "meet and greet" ticket available for Tuesday through Thursday shows only, which will set you back a cool $310, all in. But even ponying up the three bills won't guarantee you face time with Donny, since the Flamingo Box Office informed us that sometimes both performers appear, but sometimes it's only one or the other, and presumably Marie's autograph doesn't interest your sister as much.
All that said, Donny seems like a pretty down-to-earth and approachable guy, and he's often out and about taking part in charity and community events. For example, on July 25 he was at the Forum Shops at Caesars with Anthony Cools and Taylor Hicks, promoting a fundraiser for the Special Olympics. The week prior to that he was at the Flamingo welcoming Caesars Entertainment's Big Green Bus on its national eco-awareness tour, and back in June he dropped by to pay his respects to the cast of Dancing with the Stars -- Live! at the Tropicana.
Hence, your best bet is probably to keep up with the headliner's schedule via his Twitter or Facebook and find out when Donny's next going to make a public appearance somewhere. From your query, we can't tell if you're local or an out-of-towner, which would obviously make your quest that much harder. The duo has been on the road a lot lately and will not be performing again at the Flamingo until August 28, so perhaps you'll find the opportunity to run into him somewhere outside of Las Vegas.
Even if you do make it to an event that Donny's appearing at, we can't guarantee he'll want to sign your album, of course, but as we mentioned above, we get the impression that he's fairly approachable as stars go, and doesn't take himself too seriously. We wish you the best of luck on your quest -- let us know if you succeed in snagging a signature for your sis.
Images appear courtesy of Scott Roeben/CET and Langdon Flynn.
