I think you're asking the wrong question. Per sjobe, a straight "conversion" would likely be a bad idea and unnecessary to accomplish your aim of local access to data normally provided by a server reached over the Internet.
You provide two requirements:
- users must be able to access their data offline
- users must be able to sync that data with the online data store
You should think harder about how to accomplish these aims, then return to answering this question only if necessary.
You can doubtless find enough "Cocoa" applications out there that are only nominally Cocoa applications by the dubitable virtue of linking against the Cocoa framework. Cocoa is a means to an end: providing a seamless experience with your application to a Mac OS X user. If you can come up with better way to do that given your requirements and any other constraints, by all means, do it that way, Cocoa be damned.
Adobe Air is directed towards use of Flex and ActionScript. Google Web Toolkit uses Java to accomplish similar aims. There might be a good, ready-to-go option for running PHP web apps on the desktop; I don't know.
Another option might be simply having the users run your PHP web app on a local web server (Mac OS X comes with Apache and PHP). This is the route that Aigaion, which lets you manage a bibliography database, takes. The twist would be syncing with the server's data store.
In brief: don't look to "convert a PHP application to a Cocoa application"; look to satisfy your needs within the constraints of the Mac OS X platform (or the Windows platform, or the Haiku platform, or…).