I've been using Pocket Informant on just about every device for the last 10 years - from Palm to Pocket PC to iOS. It's available in the Amazon App Store ($10), but it doesn't show up under a search through the Fire store. I guess that means it's not optimized for the Fire yet. It's a good program, including both a great calendar app as well as task and contact management. I think it even syncs across devices, but I'm not 100% positive about that.
Actually it was the free app of the day on the 14th - missed it by one day. It's not worth seeing if it works for $10, I think, but maybe someone else has tried it already...