During WWII, the United States had several methods that they could have used to deliver their chemical weapons, whether mustard gas, white phosphorus, or irritants like tear gas (CS). These included air-dropped bombs and artillery shells.

To differentiate these special weapons clearly from their other variants and to make sure they were not used accidentally, after 1943, the United States adopted a special system. Explosive shells or bombs were painted olive drab with yellow bands denoting explosives like TNT or RDX. Chemical shells or bombs were painted light gray, with colored bands that indicated the type of agent they contained.

Here is one example, 105 mm artillery shells. The colored markings for 155 mm shells were the same, although the stencils were different.

http://imgur.com/mnIr0QN

Oddly, the effective 240 mm Howitzer M1 and subpar 4.5 inch Gun M1 were not authorized to fire chemical rounds, only high explosive ones

M1 HE Marking:

105 H
TNT
SHELL M1
Yellow stripes on OD

M60 FS smoke
Marking:

FS SMOKE
105 H
SHELL M60
Yellow stripes on gray

M60 WP smoke
Marking:

WP SMOKE
105 H
SHELL M60
Yellow stripes on gray

M60 H mustard gas ("CASUALTY GAS- PERSISTENT")
Marking:

H GAS
105 H
SHELL M60
Green stripes on gray

M60 CNS tear gas ("IRRITANT GAS- PERSISTENT")
Marking:

CNS GAS
105 H
SHELL M60
Red on gray

M84 HC smoke ("SMOKE")
Marking:

HC SMOKE
105 H
SHELL M84
Yellow on gray

A very common type of air-dropped bomb that could be used as an incendiary bomb (filled with white phosphorus, napalm, rubber sheets or latex) or filled with a chemical like mustard gas was the 100-pound (it actually only weighed about 70 pounds) M47 and M47A1. The M47 and M47A1 incendiary bombs came into general use in fall 1943 and were soon occasionally being dropped on German cities and factories. Fully loaded, a B-17 could carry up to 42 (the bomb-loading chart gives a loading of 40 100 lb. bombs, but since the M47 was smaller, field expedient bomb shackles were made by the Chemical Corps that allowed the the B-17 to carry more bombs)

The bomb was painted gray. If it was filled with white phosphorus, the stenciling on the bomb would be yellow, with two yellow stripes. If it was filled with mustard gas, the stenciling on the bomb would be green, with two green stripes.

Here, the bomb has purple stenciling and one purple stripe with the marking "NP", meaning it is filled with napalm.

http://imgur.com/6x1VGxF

Although the United States did not use mustard gas during World War II, an embarrassing incident showed that we were ready for all eventualities. An air raid on Bari Harbor in Italy on December 2, 1943 sunk the USS John Harvey, a Liberty ship with a secret cargo of 2,000 M47A1 mustard gas bombs. A deadly wave of mustard gas mixed with oil from the sunk John Harvey and other ships sloshed through the harbor, coating those men who were swimming away from the sinking ships, and a fog of the unknown, deadly gas hung over the harbor for days, blinding the crew of a ship who tried to sail into the harbor. The doctors who tried to treat those affected did not know they were dealing with mustard gas, and the death toll is unfortunately unknown; 83 of the nearly 700 hospitalized military patients died, but hundreds more unlucky Italian civilians could have perished.

Sources:

United States Army in World War II: The Technical Services (The Chemical Warfare Service: Chemicals in Combat), by Brooks E. Kleber and Dale Birdsell

U.S. War Department Ammunition Inspection Guide, March 2, 1944

The Day of Battle: The War in Sicily and Italy 1943-1944, by Rick Atkinson

B-17 bomb loading chart

http://imgur.com/X9EnHdB

The closest weapon that the Allies ever had to the front line was the M47A1 Bomb. It was an aerial 100 pound bomb that could carry Mustard Gas, White Phosphorus, or an early form of Napalm.

Specifically a large cache of 2000 of them were on a Liberty ship in the port of Bari in Italy for potential use when the port was bombed on December 2nd 1943 by the Luftwaffe and the ship exploded releasing the gas. In the end about 600 military personal were effected with 100 dead and only rough estimates as to the number of civilian deaths as at first nobody knew the gas was there and once discovered it was quickly hushed up and the doctors left to their best efforts, though the investigator deduced what was going on and convinced the doctors.

You're correct that chemical weapons weren't used on a large scale, though the British seriously considered deploying them on at least two occasions: in 1940, had the Germans launched an invasion, and in 1944 in response to V-1 and V-2 attacks.

As /u/the_howling_cow says, artillery shells and air-dropped bombs would have been the primary delivery systems: artillery and mortar shells of various calibres, and 65lb, 250lb and 500lb LC (Light Case) bombs.

In addition to conventional artillery, there were several Chemical Warfare Companies in the Royal Engineers. They were first equipped with rather crude projectors, later 5" Unrotated Rockets (seen [here] (http://www.iwm.org.uk/collections/item/object/205194092) being demonstrated by the 82nd Chemical Warfare Company).

Gas could also be sprayed from aircraft using Smoke Curtain Installations (SCI); [here's] (http://www.iwm.org.uk/collections/item/object/205225609) an example of an SCI-fitted Fairey Albacore. Phosgene or mustard gas could have been used in SCIs, they were also used to deploy non-toxic smokescreens, such as during the Normandy landings.

The Germans developed considerably more dangerous agents, tabun and sarin nerve agents. Again, these could have been delivered by conventional artillery, rockets or bombs. The Allies weren't aware of the nerve agents until the closing months of the war, when large quantities of tabun- and sarin-filled bombs were captured. The former primarily went to Britain, the latter to the US; the British tabun-filled bombs were eventually disposed of at sea in 1955 in Operation Sandcastle.