Green’s Dictionary of Slang

conk v.2

also konk, kunk
[conk n.1 (1)/conk n.1 (5) + echoic]

1. [early 19C; 1920s+] to hit, esp. on the nose or head, to knock out.

2. [1910s–40s] (US) to kill.

3. [1940s] in fig. use, i.e. to burden with, to assail.

4. see conk (out) v.

In phrases

conk off (v.) (orig. US)

1. [1940s] to kill.

2. [1940s+] to fall asleep, to sleep.

3. [1950s–60s] to stop work, to skive.

4. [1950s–60s] to die.

conk out (v.)

see separate entry.