Well, that's not what I was looking for since it's possible the actors could be portraying different ages, but it happens to be the correct answer. And I'm certainly not the better man star_gazer, I'm just an idiot who owns two books about the movie plus a copy of the shooting script lol.
An online copy of that script is here:
http://www.aellea.com/script/itsawonderfullife.txt
If you search for the word "newborn" it will take you to the section where it's related by the the angel Joseph that the Bailey's first child is a boy, followed by a girl, then a little later on it says they were followed by "two more babies."
So the oldest child is either Pete or Tommy. A quick look at the two makes it evident that it's Pete, but I have proof coming later. Pete older than Janie makes sense in reality, since as dj168 listed the actor who played Pete is a year older than the actor who played Janie. Also, if you watch the Youtube link at about the 3:30 mark (and especially at about 3:44) you'll see that Pete is a head taller than Janie, which I know contradicts your opinion star_gazer about who is taller, but I dunno, it's pretty conclusive to me lol.
Also as dj168 pointed out, there's a large jump in the ages between Janie/Pete and Tommy/Zuzu. (1934/35, vs 1940/41)
So most likely the proof that the 2nd born, the girl, is indeed Janie and not Zuzu is by simply looking at them, but we also have star_gazer's wiki reference stating "George Bailey (James Stewart), Mary Bailey (Donna Reed) and their youngest daughter Zuzu (Karolyn Grimes)."
So I'm sure it's agreed that Zuzu is younger than Janie, making Janie the 2nd child, the "girl" referenced in the script.
Those two (Pete/Janie) were the hard part of the question to me, but we've got another proof to make:
Zuzu is not the youngest child.
That wiki reference above states she is the youngest daughter, and that is correct. But she is not the youngest child, Tommy is.
I noticed there are about 3-4 web pages that refer to Zuzu as the youngest child, including a wikipedia one that uses that same photo with the word 'child' replacing 'daughter'
https://en.wikipedia.org/wiki/George_Bailey_(fictional_character)
But there are many more like the first wiki one that refer to her correctly as "youngest daughter"
A site dedicated to the actress makes no mention:
http://www.zuzu.net/
Jimmy Hawkins, who played Tommy, was 4 years old when the movie was shot, Karolyn Grimes was 5, or 16 months older.
In the same video, you can tell he's younger than she. She's started school, walking home from which she catches cold, he still runs around tugging on his father's pants leg. (from an earlier scene, where he keeps saying "excuse me" because he burped.)
But there are further proofs:
In the "Making of" book it specifically gives the Tommy character the age of 4 in the movie, and refers to him as the youngest. (I know there's no online reference of this)
Jimmy Hawkins' wiki page lists him as playing "4 year-old Tommy" in the movie:
https://en.wikipedia.org/wiki/Jimmy_Hawkins
The online proof is here:
Jimmy Hakwins wrote a book about the movie, and on the inside front flap it reads "Jimmy Hawkins played Tommy Bailey, the youngest of the Bailey children."
This is a link to Amazon, you have to click on "front flap" after to read it.
http://www.amazon.com/Its-Wonderful-Life-Favorite-Classic/dp/0740738410#reader
This also clears up any possibilty that Tommy was older than Pete, which is why star_gazer when you asked if there was any evidence that you had Pete and Tommy in the wrong order I replied no, because you were right, Pete is older than Tommy. (I hope you understood that's what I meant :-)
The correct order is indeed:
Pete
Janie
Zuzu
Tommy
