A method I have used in the past is to have 2 files: the file containing the list data and a version file. Use HTTP library to download the version file and check against current version. If it's bigger, download the list file.
As for uploading both the files, use the FTP library (incrementing the number in the version file before uploading).
Alternatively, I'm pretty sure the FTP library allows you to get the last modified date of a file.
For either of those methods you will need web space, specifically one that offers FTP access. Most free hosting providers offer FTP access but they can be somewhat unreliable.