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To start off, if a gun is Stopping Power Friendly then that means that using Stopping Power will kill your enemy with (one) less bullet(s) then usual.
I made a list of all of the guns in MW2, their known damages, and then did some math and got their new damages with stopping power. Please note that these are the commonly excepted gun damages, but they might not all be exact.
Also note, these damages are based on normal game modes where the player has 100 damage to start with. It does not take into account Painkiller, damage bonuses for Head Shots, or Hardcore game modes.
For the hardcore modes (where you start with 30 health), most guns are a one hit kill normally, so they are not Stopping Power Friendly. If a gun is not usually a one hit kill, then it will be Stopping Power friendly in Hardcore. Pretty simple there
The list is in this format:
M4A1 (30-20) (42-2

(Yes, Yes)
Gun Weapon (Close Range, Distance) (Close Range w/ SP, Distance w/ SP) (Difference at Close Range?, Difference at Distance?)
So for this example the gun is (obviously) the M4A1.
It normally does 30 Damage at Close Range, and 20 Damage at a Distance. With stopping power, however, it does 42 Damage Close and 28 Far.
So at Close Range, it takes 3 Bullets to kill w/ SP and 4 w/o it.
Therefore, it is Stopping Power friendly at Close Range.
At a Distance, it takes 4 bullets to kill w/ SP and 5 to kill w/o. So at a Distance, it is also Stopping Power Friendly.
In the end, it comes down to how you will use the gun. If you're planning on sniping with the M4A1 (good luck!) then go for stopping power. If you're not, then use some other 2nd-Tier Perk.
If you didn't read any of that, a quick summary:
If a weapon has (Yes, Yes) after it, then it is Stopping Power Friendly everywhere.
If a weapon has (Yes, No) or (No, Yes) Then it is Half-Stopping Power Friendly. You can decide whether or not to use SP based off of if you'll use the weapon at close or long range.
If a weapon has (No, No) then you should not use Stopping Power with that gun. It won't make an impact.
List:
M4A1 (30-20) (42-2

(Yes, Yes)
FAMAS (40-30) (56-42) (Yes, No)
SCAR-H (40-30) (56-42) (Yes, No)
TAR-21 (40-30) (56-42) (Yes, No)
FAL (55-35) (77-49) (No, No)
M16A4 (40-30) (56-42) (Yes, No)
ACR (30-20) (42-2

(Yes, Yes)
F2000 (30-20) (42-2

(Yes, Yes)
AK-47 (40-30) (56-42) (Yes, No)
MP5K (40-20) (56-2

(Yes, Yes)
UMP45 (40-30) (56-42) (Yes, No)
VECTOR (25-20) (35-2

(Yes, Yes)
P90 (30-20) (42-2

(Yes, Yes)
MINI-UZI (30-20) (42-2

(Yes, Yes)
L86 LSW (40-40) (56-56) (Yes, Yes)
RPD (40-40) (56-56) (Yes, Yes)
MG4 (30-30) (42-42) (Yes, Yes)
AUG HBAR (40-40) (56-56) (Yes, Yes)
M240 (30-30) (42-42) (Yes, Yes)
INTERVENTION (70-70) (98-9

(No, No)
BARRETT .50 CAL (70-70) (98-9

(No, No)
WA2000 (70-70) (98-9

(No, No)
M21 EBR (70-70) (98-9

(No, No)
*There are a lot of factors affecting a sniper rifle's damage. Although statistically SP shouldn't help them, using it is usually a good idea.
[EDIT]: There have been a lot of people concerned with the fact that sniper rifles aren't shown here to be affected by SP. I figured out why, and I'm sorry it took me so long to do so.
Sniper rifles get bonuses for hitting people in certain parts. With a headshot, the damage is 1.5x greater, with a bodyshot, 1.1.
70 is the damage you get without one of these multipliers.
So take a look at what happens when you were to get, say, a bodyshot.
(A bodyshot is a hit anywhere besides the head, chest, and limbs)
INTERVENTION (77-77) (107.8-107.

(
Yes, Yes)
Therefore sniper rifles are Stopping Power friendly if you hit the enemy in the body. Anywhere else, they will be either a one shot kill (head, chest) or two shot kill (limbs) with or without SP.
Well that's it, hopefully this should help some people out in the game (after making this list I've already taken SP off of four of my ten classes)