I was doing some snooping around looking for additional information for our hunt this year and came across this website devoted to Coues deer. Good place to start some research on these somewhat mysterious deer, well at least in Arizona.
Now, as far as the .223 and the .22-250 for Coues deer, I would only opt for the .223 if your hunt was a sure thing and a sure shot at 200 yards or under. You can use the 60 grain Nosler Partition or the new 65 grain Sierra GameKing. My suggestion for powder is IMR-4895, V V N-135 and AA-2520. The .223 would not be my first, second or third choice for hunting Coues.
The 22-250 would be a slight improvement over the .223 since you get the obvious boost in velocity. Coupled with the 65 grain Sierra GK, I would use IMR/H-4350, AA XMR-4350 and V V N-550. Again, I would limit these shots to 250 yards or under for the sake of safety and surety. I know that it sounds like I'm being overly cautious and I am.
The success rate in the southern zones is not very high for the Coues or the Mule deer in Arizona due to the drought that has been plaguing the state for the last 23 years. It is a little better in the northern zones but not a bunch. Game and Fish finally realized that the success rate was miserably low due to the lack of game, from the absence of water (bright guys, huh), so they have been reducing the number of tags significantly, for the last 3 years.
If you get drawn, I would suggest that you start with something in the 6mm/243 range, a cartridge with some horsepowder combined with a well made bullet. I'm getting good results from the 6mm Rem. and the 240 WBY using the Barnes 85 grain TSX. Some of the shots that I've seen though, have been in the 4-500 yard range.
My choice is coming down to the .257 RSAUM and the 100 grain TSX bullet, I think. It is showing lots of velocity and remaining energy with good accuracy at 500 yards. There are a couple of others still in the running and I have some more testing to do, yet.