1997:
Why date the D.C. Animated universe at all? Shouldn't it be timeless?
Firstly, I know there are a significant number of fans who feel that the collective series of the DCAU should remain timeless; that no year or date of any kind should be ascribed to them as they should always be viewed as taking place in the near or far future, so as to keep them relevant to the time we live in now. I'd be fine with that, except the shows themselves often give clear dates as to when certain events happen, and to ignore that seems silly. It makes more sense to me to fit those dates together in a logical way, and just accept that the D.C. Animated Universe is not the universe that you and I live in. We don't have and never will have these superheroes. And for me, laying down the order and times at which I think things happened (based on the episodes) does nothing to ruin the idea that these things will one day happen. They won't happen. It's as simple as that.
Why these episodes? Why this order?
After splitting Superman into three 18 episode sections I started mixing the 24 episodes of The New Batman Adventures into the series, starting at the end, alternating episodes of Batman & Superman. There are far more episodes of Superman than Batman so to help extend Batman's run I counted any Superman featuring Batman as a Batman episode. This allowed for a nearly perfect balance between the two shows for two years of Superman's run (from my perspective). This also placed the Batman episode "Cold Comfort" in year 2 (the latest I could place the episode), which features a date of August 20, 1997 within the episode. Because in my timeline there's only 1 year between Batman: The Animated Series & The New Batman Adventures I decided that I'd delay Dick Grayson's appearance in this season for as long as I felt I possibly could, and since his return marked the first appearance of Tim Drake as Robin he'd have to be delayed as well. I cross referenced all the episodes in which Robin (Tim Drake) & Nightwing (Dick Grayson) did NOT appear, then allowed for continuity and some personal preference, choosing 6 of these episodes to air before Tim / Dick arrive on the scene (in "Sins of the Father"). With Superman added to the mix I managed to delay Dick's first appearance to the thirteenth episode of the season.
106 4x15 Cult of the Cat
While toying with what episode to place first in this section, I had to choose an episode that didn't feature Tim Drake or Dick Grayson. I also wanted one that demonstrated the passage of time since the last episodes of Batman: The Animated Series; this episode seemed perfect. It features Catwoman, a character we know well from the previous series, but in a new guise. She & Bruce discuss the changes they've gone through in dialogue. I had once considered this as Catwoman's final appearance, as it gives her a kind of happy ending, but we know from Gotham Girls & Catch Me that Selina returns to her life of crime...so saving this for her final appearance seemed pointless. Also, her dialogue with Dick in "You Scratch My Back" suggests it takes place after this installment in which Catwoman claims to have changed.
107 2x01 Identity Crisis
108 4x04 Double Talk
Lois Lane & Clark Kent cameo in the background of this episode.

109 2x02 Target
110 4x20 Mad Love
111 2x03 Action Figures (1 year after The Way of All Flesh)
112 4x10 Torch Song
113 2x04 Mxyzpixilated
114 4x13 Mean Seasons
115 2x05 Double Dose
116 4x11 The Ultimate Thrill
117 2x06 Solar Power
118 4x02 Sins of the Father
*Tim Drake / Robin II introduced.
*Dick Grayson / Nightwing reintroduced.
119 2x13 Father's Day (June 15, 1997 - about half way through the year)
120 4x08 Growing Pains
Has to take place before "Holiday Knights" as both episodes feature Clayface, yet his return from his apparent death in "Mudslide" is explained here. The story features Tim Drake as Robin and so must take place after "Sins of the Father".
121 2x07 Monkey Fun
122 4x05 You Scratch My Back
An early Dick Grayson appearance. We know this because Barbara has a surprised reaction to Nightwing's wings. And since the story features Dick it has to take place after "Sins of the Father".
123 2x08 Brave New Metropolis
124 4x03 Cold Comfort
The Date is given during this episode via a (television appearance of Bruce Wayne) as August 20, 1997.

Setting this episode a few episodes after Superman's "Father's Day" which is set on June 15, 1997 seemed to make sense.
125 2x09 Ghost in the Machine
126 2x10 World's Finest, Part I (Harley Quinn, Joker, Alfred, Bruce / Batman)
127 2x11 World's Finest, Part II
128 2x12 World's Finest, Part III
129 2x14 The Hand of Fate (introduces Dr. Fate)
130 4x07 Joker's Millions (1 month after World's Finest, Part III)
131 2x15 Bizarro's World
132 4x24 Judgment Day
133 2x16 Prototype
134 4x01 Holiday Knights (after Growing Pains - December 1997)