Green’s Dictionary of Slang

1. a Bell’s whisky [pun].

1984

‘Derek Raymond’ He Died with His Eyes Open 111: ‘What’ll it be?’ [...] ‘Ring-a-ding’ He uncapped a bottle of Bell’s, got a glass and some ice and slapped the lot on the counter.

2. (US police) a telephone.

1987

M. McAlary Buddy Boys 192: ‘I got some information,’ Gallagher said. ‘All right,’ Henry replied. ‘Tell me.’ ‘Not on the ring-a-ding’.