The Slang of Sleep


GB  COHA  COCA  First occurance (GB) 
 Snooze  46438  379  577 1811 had taken my after-dinner snooze
 Nod off  16550  109  315 1835 After a minute's silence, he nodded off the whimsical intruder

1841 and then, in the midst of these reflections, nodded off into another slumber

 [Call] it a night  6597  49  120 1841 I call it a night of rejoicing

1866 We'll call it a night's work and quit

1919 I'm tryin' to make him call it a night so's I can hit the hay

 Tuckered out  6089  111  38  1837 For the first four or five hours, we marched rather too fast, and got pretty nigh tuckered out
1Forty winks      5041 52  7       1830 Even the invalid, if he can, will do well to avoid his " forty winks' nap" at noon

2[sleep] like a log

 5022  39  8  1830 Then he went home and slept like a log.
 Hit the sack      4043  35 57 1910 Or a large paper sack filled with wrapped bonbons is hung between folding doors, each child blindfolded in turn, given a cane and instructed to hit the sack if he can

1940 Half the crew (those with even billet numbers) were told they could hit the sack until called for

3Count sheep  3642     27  46  1831 Wiese went outside the door to count sheep with the samboc.

1875 Either the excitement of the evening, or the over-fatigue, propped my eyes wide open, and I lay there and turned and twisted, counting sheep forward, jumping over the fence, and backward, jumping back

 Hit the hay  2953  38  28 1830 [he] can hit the hay -stack with the best of us

1868 only the musketry of the Bavarians was still rattling, but they only hit the hay 

1903 We were both tired, and voted about ten hours rest was what was needed, and when that was inscribed on the register we hit the hay

 4Zonked out     1118  7  10  1956 as a nurse zonked out on booze

1983 by the time we'd played another kickball game and seen a film on bats in the recreation room, I was zonked out.

 [to be] out like a light  905 10  14  1831 she was out like a LIGHT on the floor of our favorite watering-place
Beddy-bye 43  7  5   1940 who's going to wipe their little moufies off and rock them to beddybye after they have their frog pancakes?
1Forty winks, meaning to take a short nap, could come from the expression "I couldn't sleep a wink" used all the way back in the 1500s according to the OED. A wink was taken as the smallest possible amount of sleep. 
2 and a few other interesting things you can "sleep like"
For your "gee whiz!" collection, counting sheep doesn't actually help you fall to sleep. A study at Oxford University found that thinking about waterfalls and beaches (relaxing things) actually puts you to sleep faster.
4 "Zonked out" was originally used as a drug term in the '60s and '70s. In the '80s you see it more in relation to sleep, but it still often holds on to the drug related meaning.