When I try to 'Go online' or 'Sync with Online Database', DayLite refuses to do the sync and complains that the time is not within a reasonable threshold.

If you are performing online/offline syncs, then it is critical that all the date/time settings on all computers are the same (or within 1 minute of each other). The best way to acheive this is to set your computer(s) to use Network Time.

Go to the System Preferences -> Date & Time and select to use Network Time Server (time.apple.com for example). Also ensure that you are setting the correct timezone for each computer. The synchronization process will take the timezone into consideration.

Make sure all computers are on Network Time.