The SIG Sauer P320 is a 9mm pistol, but Payday and COD are wildly inconsistent with how powerful a 9x19mm weapon is.
I decided to go with the Payday 9mm approach but with a few tweaks to make it feel not as much of a peashooter without pistol skills.

The damage sits at a base of 61, boosted to 64 by the generic perk deck passive. This is more powerful than the other 9mm handguns (M9/Bernetti, Glock 17/Chimano 88, etc) and should give you solid 4 shot headshots without skills or attachments.
The fire rate sits at a base of 500 RPM, in between the 480 RPM that most of the 80 damage pistols use, and the 545 RPM that most of the spammy 9mm pistols use.

Total ammo capacity is noticeably lower than existing 9mm pistols at 6 total magazines (102 bullets total) and base ammo pickup is set 2-4 bullets per pickup. This is somewhat weaker than existing 9mm pistols, but is a tradeoff for the greater damage that the P320 inflicts.

Accuracy is acceptable at a base of 56.
Stability is average at a base of 52, but it should be a non factor when the kick is rather rather low and the generally small engagement ranges that Payday has.

Magazine size is above average at a base of 17 and options for increasing the mag sizes to even further beyond 17 rounds. The 32 round mags/mags with .40S&W Hollow Point don't line up with ammo capacity in real life/MW2019 due to vanilla Payday extra ammo functions being a bit weird.

Concealment is somewhat subpar for a spamming pistol at a base of 28, but the existing concealment boosting mods should bump you back up to the low 30s in concealment.

True to its appearance in MW2019, you get a variety of weapon mods to use: triggers, slides, and griptape. Blueprint cosmetic options are available through Weapon Painter.

If you prefer a harder hitting P320, use the Br* tsh Superhero Caliber, .40S&W Hollow Point. .40S&W Hollow Point will bump up your damage to the 85 damage range, but reduces your total ammo supply and reduces your ammo pickup to 1-4 bullets per pickup.