I wasn't efficiently dealing with riot zombies and haven't found any good resources online for how to do so, they were either not as effective as advertised, or did not include new guns, so I decided to hop in a solo game and test all guns one by one against riot zombies and draw my conclusions from there. All tests have been done on nightmare difficulty

Surprisingly all melee weapons proved themselves quite good even on nightmare difficulty. As higher difficulty riot units don't stagger from bullets, melee is particularly useful since it does stagger using heavy attacks, giving more time to switch weapons or hold out safely until an team member helps you out. Ammo conservation is another strong argument for carrying one of the weapons below in your kit.
tip: when using melee, wait for the riot unit to recover before striking, to stagger him again without getting scratched

• Hammer - by far the best melee weapon, breaking the helmet in a single swing
  
  
• Axe - takes quite a bit of time to get used to, since it requires to aim weirdly high to hit the head, if you get the hang of it, you can consistently break the helmet in two hits.
  
  
• Baseball bat, crowbar, guitar, kabar, machete, scythe, wrench - all take about three hits to break the helmet
  
  
• Banjo, golfclub - takes about four hits to remove the helmet

• Deagle - kills the riot unit in a single shot
  
  
• Arlene revolver - breaks the helmet in about 8 shots
  
  
• 1911 - breaks the helmet in about 20 shots
  
  
• Sig - breaks the helmet in about 35 shots

• Mac-10 - removes the helmet in about 30 shots
  
  
• MP5k - about 45 shots
  
  
• KG9 - about 60 shots

Since shotguns are very range dependant, the closer you are the more damage they do. In my tests I was shooting from a safe (~2m) distance, so the values more realistically reflected actual usage.

• Double barrel - removes the helmet in one shot which uses two shells
  
  
• Remington 870 - about 4 shots
  
  
• Mossberg 590 - about 5 shots
  
  
• Benelli M4 (semi-auto) - about 6 shots
  
  
• Over under - about 11 shots

• SCAR - about 30 shots
  
  
• AR-15 - about 30 shots
  
  
• AK-74u - about 38 shots

• Remington 700 - 7 shots
  
  
• Browning Lever Action Rifle (BLR) - about 8 shots
  
  
• M1 Garand - about 9 shots

• Bow, crossbow - single shot to kill
  
  
• Explosives - single 'shot' to kill, although this method is super loud and will attract a horde in no time
  
  
• Flamethrower - about 15.. ammo? capacity?, whatever it's measured in, it takes about 15 of those to kill a riot unit asap, could be less if used sparingly