The People of Gibraltar
1704 - Devil's Bowling Green – Rock Strewn and Rough 

Before the late 19th century, there was a steep sloping cliff formed by the accumulation of rock debris just above two beach-like areas on the south-west coast which would eventually be known as Camp Bay and Little Bay. It was known as the Devil’s Bowling Green.

Devil's Bowling Green    ( 18th century – Unknown )

The name probably came into usage during any one of Gibraltar’s Sieges after the Anglo-Dutch takeover in 1704. It was certainly in use during the Great Siege (see LINK) - an ironic reference to its rough surface and the fact that enemy cannon balls would often land there and roll down the rocky surface. 
Three of the enemy’s shot came on shore. One fell at Europa, one at the Devil‘s Bowling Green . . . (1779 - Samuel Ancell - A Circumstantial Journal)  (See LINK) 
Buena Vista from Devil’s Bowling Green - Author’s decription    ( 1779 - John Spilsbury  ) (See LINK)
There are also multiple mentions during the 19th century:
He had also in his turn the command of the Brigade of Engineers, a part of which was encamped on the Devil's-Bowling-Green, so called from the extraordinary roughness of the ground : it is about 300 feet above the sea  . . (1812 – The Royal Military Calendar – Vol 3) 
The “He” refers to Lieutenant Colonel William Booth who was later appointed Quarter Master by the Governor of Gibraltar General Eliott and served in Gibraltar during the Great Siege until 1782. 

The date of this painting is unknown to me but it was either painted or represents Gibraltar in the early 19th century and shows the Devil’s Bowling Green with its cliff “300 feet above the sea” - On the left it is overlooked by another outcrop on to which Buena Vista Barracks would later be built. The ridge of the Rock is crowned by Signal Station on the left and O’Hara’s Tower (see LINK) on the right  

The only reference I can find of the Bowling Green being called an Alley is by R. Stewart Paterson: (see LINK)
The Devil's Bowling Alley or Green, a rock strewn and rough piece of ground between Europa Pass and the cliffs overlooking Quarry Bay and to the south of Buena Vista barracks.  (1884 - Notes and Queries for Literary Men)
The “Quarry Bay” comment is interesting as it predates by a few years the eventual destruction of the “Green” during the very late 19th and early 20th century when the entire Devil’s Bowling Green disappeared when the cliff-face was mined and quarried for stones that were used during for the building of Gibraltar’s dry docks, the detached mole and its new dockyard. 

The cliff-face of the Bowling Green being quarried for stone – The harbour in the middle distance shows that the Detached Mole – begun in 1888 and completed in 1901 - had not yet been built. This being Gibraltar, the locals almost immediately renamed the entire area “el Quarri”. Rather indiscriminately there was a tendency to include Camp Bay in this catch-all name.

South end of Camp Bay looking south towards Little Bay ( 1930s )

Little Bay during WW II

“Before and after photographs” of the cliff - by the very early 20th century the Devil’s Bowling Green  had complete disappeared, many of its quarried stones propping up new structures of one sort or another in newly enlarged and improved  harbour.

In 1900 Frederick George Stephens (see LINK) in his History of Gibraltar also thought the place worthy of a mention:
Thence the Rock sweeps down by the Devil's Bowling-Green - so named, on the lucus a non lucendo principle, from its rugged surface — to Little Bay . . . . . A range of granite mountains in Argyllshire is similarly named the Duke of Argyll’s Bowling-Green. 
Not a particularly good comparison as the Scottish name is a corruption of the Gaelic Baile na Grèine, a large area of Argyll that includes dozens of tall mountains – many of them taller than the Rock.

In 1859 a two-gun battery that looked over Little Bay was named The Devil's Bowling Green Battery. It was close to the sea and was overlooked by both the Buena Vista Battery and the seven guns of the Europa Pass Battery.