Here are four Constantine The Great coppers I cleaned up recently. The one with Winged Victory on the reverse is really cool and two of the others show a Roman soldier spearing his foe!!! It was a tough period Bone
Bone,two of them are Constantine the Great but the skinny guy top left is probably a son or later descendent with the family name.Constantine is always pictured as a big beefy dude.I would be interested to see a closer-up photo of the bottom left coin.Looks like a female.
And I think this is your bottom right coin because I think I can see DNVALEN from 8 to 11 O'clock,the portrait looks similar and the reverse is the same.
I agree with your first choice, Constantius II. The second one, the bust with the long hair I'm still looking for but I do recall it somehow being related to Constantine??? It does have a chariot on the reverse too.
I think I found the coin and you were right,it's Constantine I. Constantine the Great, deified, AE 3. 337-340 AD. DV CONSTANTINVS PT AVGG, veiled head right / emperor driving quadriga right, the hand of God reaching down to him, SMALT in ex.
I agree with Mikjo0, top left is Constantius II, son of Constantine the great. It cannot be Constantius Gallus, who is always represented bare head, and you can see a diadem. Bottom left is constantine the great, a commemorative coin struck after his death. Bottom right should be Valentinian I or II, I can't say more(I'm at work with no books) Cucumbor
For the top right one, I would say Constantius Gallus, FEL TEMP REPARATIO reverse and Constantinople mint, similar to the one below (courtesy of Wildwinds)