Here is my personal view of the DCAU Timeline. Keep in mind, I haven't seen all of them, so this is just the shows I have seen, or at least information from between series.
Batman: The Animated Series, "Beware the Gray Ghost"
Batman: The Animated Series, "Feat of Clay"
Batman: The Animated Series, "Mudslide"
The New Batman Adventures, "Growing Pains"
The New Batman Adventures, "Holiday Knights"
Mr. Freeze Story Arc.
Batman: The Animated Series, "Heart of Ice"
Batman: The Animated Series, "Deep Freeze"
Batman & Mr. Freeze: SubZero
The New Batman Adventures, "Cold Comfort"
Batman Beyond, "Meltdown"
Ra's al Ghul Story Arc.
Batman: The Animated Series, "Off Balance"
Batman: The Animated Series, "The Demon's Quest"
Batman: The Animated Series, "Avatar"^
Batman: The Animated Series, "Showdown"^
Superman: The Animated Series, "The Demon Reborn"
Batman Adventures, Issue #4
Batman Beyond, "Out of the Past"
^ There is no evidence as to which of these two episodes take place first, so as of now, I will just label them by production order.
Batman and Harley Quinn Event
Justice League, "Wild Cards"
Harley Quinn and Batman, Issue #1
Harley Quinn and Batman, Issue #2
Harley Quinn and Batman, Issue #3
Harley Quinn and Batman, Issue #4
Harley Quinn and Batman, Issue #5
Justice League Unlimited, "Task Force X"^
Batman and Harley Quinn
Batman and Harley Quinn, Issue #3
Batman and Harley Quinn, Issue #2
Batman and Harley Quinn, Issue #4
Batman and Harley Quinn, Issue #1
Batman and Harley Quinn, Issue #5
Batman and Harley Quinn, Issue #6
Batman and Harley Quinn, Issue #7
Justice League Unlimited, "Flash and Substance"
^ This placement is because Harley Quinn and Batman is stated to take place during Justice League and is hinted by Harley in the movie itself that it's been a while since she's been released on parole.
