Probably one of the most common and widely used would be the Uzi and Micro Uzi setups. They are bullet hoses on full auto but still controllable. They are pretty much able to run any 9mm can out there and are known for reliably cycling the heavier 147gr subsonics.

3144810
This technically isn't a submachine gun but maybe the Mac-10?

http://en.wikipedia.org/wiki/MAC-10

I'll be honest and admit I don't know much about submachine guns in general. Just wanted to see if I could help.

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M3A1 Grease Gun
Can't go wrong with a classic
[In service 1942–1992 (US) and 2004-???? (Philippines)]

KRISS Vector
New (felt) recoil dampening tech.

British STEN
You can make these IN A CAVE WITH A BOX OF SCRAPS! (Tony Stark Optional.)

3145349
Sorry I couldn't help out. Thanks for the video though, Hickock45 is always cool.

3145371
I wasn't kidding when I said a STEN could be made from a box of scraps. The Human Resistance could easily make them themselves much like the Maquis and other resistance groups did in WWII.

3145376
3145381

EDIT: Fimfiction screwed up the video. http://youtu.be/FImgqhivLBw?t=10s

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#1: It cannot be the MP5.

Fuck, man, that's harsh. And you're making us stick with 9x19.

#2: It cannot be the UMP9 (or feature a similar polymer receiver).

Welp, there goes my chance for a more modern SMG.

I have to go with the full size Uzi, since you ruled out 7.62 and 9x18 guns.
My second choice is PM-65 RAK. It is very concealable and is less bulky than any of the other suggestions.
My third choice is the L2a2 Sterling SMG.
My fourth choice is the Beretta M12.
The Daewoo K7 looks ideal for stealth.
SA 23 is the inspiration for the Uzi.
Upon Hans informing me about it, I absolutely nominative the PP-19 Vityaz.

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Carl Gustav M45
If it's good enough for the US Navy SEALs it's good enough for your story.

3145506
Is it just me or does the CBJ-MS look like it has two mags?

3145561
Derp, I forgot all about that one; I thought it was just another iteration of the Bizon.

3145718

Post updated.

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The PP-2000, the SMG/machine pistol that is determined to be a PDW/carbine.
Because before CBJ was rendering 4.6 obsolete, 7N31 was making 5.7 cry in the corner without any lube.
Oh, and it can be rechambered into 6.5CBJ, because the MP7 wasn't sad enough, we need more of its sauerkraut flavored tears.

...And I love that you can use its 44round mags as a stock, and that the fancy polymer weapon has a piece of pipe with a wedge as a stock.

Failing that, there's the SR2 in 9x21

And since we're just upping the 9mm cases, let's go with the SR3 and get the whole family together

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MP5 or UMP .45

3147790

What?.....Meh its only sweetie belle

3147804

Kay. Just the UMP .45

3147790
You think 5.7 deserves lube?

3148429
More lube than 4.6mm.

3148734
I'd prefer not being on the lower ends of prison love.
5.7 on the other hand, needs all the dry, splintery tree branch anyone can give it. Spitting on said branch would be far to polite to afford to give that cartridge.

3150045
I can't rightly say I would mind being on the upper hand of 5.7 worshipers or a certain Mr Stoner...

....I'm sounding like a fag now, but they really deserve it...

3150512
Well, it was the bastard child of Stoner, who chambered an AR in .308.
There's nothing remotely M14-ly in there. Suggesting such is an insult to M14s!

3153607
A lot of things have wood furniture.

3144810
Hmm, that's a tough one.

The only 9x19 SMGs I can think of right off the bat are the MP40, Sten gun, and M3 "Grease gun". However, they don't match your requirements all too well. All three are fired from an open bolt and I don't think the MP40 can mount a suppressor. The M3 did have the capability to accept a flash hider, but that's not really a suppressor. They did however, manufacture Sten guns with integral suppressors. The cons to this though, were that it had a reduced muzzle velocity and it tended to overheat.

Beyond that, I only really know of the Steyr TMP machine pistol. It's made of synthetic materials, feeds from detachable box magazines, has a fore grip, a 5" barrel, and can mount a suppressor.

Considering what I know and what you're looking for, I'd recommend the TMP if you want something a bit more modern. The Sten is a goodie, but it's also an oldie, perhaps too old for what you're looking for.

3154646
Still a better gun than the Luger.

3158369
Wasn't the Grease Gun in .45?

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3162240

The M3 SMG was manufactured in both .45 and 9mm during WWII. The .45 model was to replace the heavier and more expensive Thompson in frontline service, while the 9mm version was made and delivered to the OSS. Conversion kits were also made, so that the .45 variants could be converted to 9mm if desired/needed.

It appears that the 9mm conversion kits gave the weapon the ability to use British Sten magazines, but I actually don't know why they made some in 9mm to begin with. Perhaps to share common ammo with the Brits or used captured German 9mm?

3162538 Huh, didn't know about wound cavity size. I don't really care about the whole 9mm vs. .45 debate, so I'll steer clear of it.

I'm just confused about why the US army would chamber the weapon for 9mm (albeit only a small number) to begin with. The standard smg/pistol caliber for the US was .45 ACP, and I don't recall any 9mm weapons being issued to American forces in any quantity. The M3 was supposed to replace the Thompson, so it seemed they had no interest in a different caliber of weapon. All the army wanted was an smg that fired .45 ACP and was lighter and cheaper than the Thompson.

Unless, they just made it for the Brits. I honestly don't know, I cannot find anything about why some were chambered for 9mm.