Green’s Dictionary of Slang

a poor shot; thus Peter Gunner who will kill all the birds that died last summer.

1614		Cold Year n.p.: It was a shame that poore harmlesse birds could not be suffered to save themselves under a bush... but that every paltrie Peter-gunner must shoote fire and brimstone at them [F&H].
1628		J. Shirley Witty Fair One II ii: I smell powder... this peter-gunner should have given fire [F&H].
c.1786		Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Peter Gunner, will kill all the birds that died last summer. A piece of Wit commonly thrown out on persons walking through a Town with a gun in their hand.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn) n.p.: Peter Gunner, will kill all the birds that died last summer. A piece of wit commonly thrown out at a person walking through a street or village near London, with a gun in his hand.
1811		Lex. Balatronicum [as cit. 1788].
1862		E. de la Bédollière Londres et les Anglais 316/2: peter gunner, Peter gunner will kill all the birds, that died last summer Pierre le canonnier tuera tous les oiseaux qui sont morts l’été dernier.