Heart Gold and Soul Silver have an IR port on them, which is on top of the save chip, so that it is a little harder to access the save.
The Action Replay DSi is unable to read/write to it, but there are alternatives:
The NDS Backup Adapter Plus: http://www.consolesource.com/ecomm/catalog/NDS-Backup-Adapter-Plus-p-3018.html
And this: http://projectpokemon.org/forums/showthread.php?12405-A-tool-to-backup-HG-SS-saves
Oh, and there's another alternative:
http://gbatemp.net/index.php?showtopic=215641
Do that, and it should be readable by the ARDSi.