From Cab Calloway's Hepster Dictionary, published in 1940

Guitar: Git Box or Belly-Fiddle
Bass: Doghouse
Drums: Suitcase, Hides, or Skins
Piano: Storehouse or Ivories
Saxophone: Plumbing or Reeds
Trombone: Tram or Slush-Pump
Clarinet: Licorice Stick or Gob Stick
Xylophone: Woodpile
Vibraphone: Ironworks
Violin: Squeak-Box
Accordion: Squeeze-Box or Groan-Box
Tuba: Foghorn
Electric Organ: Spark Jiver

A hummer (n.) - exceptionally good. Ex., "Man, that boy is a hummer."
Ain't coming on that tab (v.) - won't accept the proposition. Usually abbr. to "I ain't coming."
Alligator (n.) - jitterbug.
Apple (n.) - the big town, the main stem, Harlem.
Armstrongs (n.) - musical notes in the upper register, high trumpet notes.
Barbecue (n.) - the girl friend, a beauty
Barrelhouse (adj.) - free and easy.
Battle (n.) - a very homely girl, a crone.
Beat (adj.) - (1) tired, exhausted. Ex., "You look beat" or "I feel beat." (2) lacking anything. Ex, "I am beat for my cash", "I am beat to my socks" (lacking everything).
Beat it out (v.) - play it hot, emphasize the rhythym.
Beat up (adj.) - sad, uncomplimentary, tired.
Beat up the chops (or the gums) (v.) - to talk, converse, be loquacious.
Beef (v.) - to say, to state. Ex., "He beefed to me that, etc."
Bible (n.) - the gospel truth. Ex., "It's the bible!"
Black (n.) - night.
Black and tan (n.) - dark and light colored folks. Not colored and white folks as erroneously assumed.
Blew their wigs (adj.) - excited with enthusiasm, gone crazy.
Blip (n.) - something very good. Ex., "That's a blip"; "She's a blip."
Blow the top (v.) - to be overcome with emotion (delight). Ex., "You'll blow your top when you hear this one."
Boogie-woogie (n.) - harmony with accented bass.
Boot (v.) - to give. Ex., "Boot me that glove."
Break it up (v.) - to win applause, to stop the show.
Bree (n.) - girl.
Bright (n.) - day.
Brightnin' (n.) - daybreak.
Bring down ((1) n. (2) v.) - (1) something depressing. Ex., "That's a bring down." (2) Ex., "That brings me down."
Buddy ghee (n.) - fellow.
Bust your conk (v.) - apply yourself diligently, break your neck.
Canary (n.) - girl vocalist.
Capped (v.) - outdone, surpassed.
Cat (n.) - musician in swing band.
Chick (n.) - girl.
Chime (n.) - hour. Ex., "I got in at six chimes."
Clambake (n.) - ad lib session, every man for himself, a jam session not in the groove.
Chirp (n.) - female singer.
Cogs (n.) - sun glasses.
Collar (v.) - to get, to obtain, to comprehend. Ex., "I gotta collar me some food"; "Do you collar this jive?"
Come again (v.) - try it over, do better than you are doing, I don't understand you.
Comes on like gangbusters (or like test pilot) (v.) - plays, sings, or dances in a terrific manner, par excellence in any department. Sometimes abbr. to "That singer really comes on!"
Cop (v.) - to get, to obtain (see collar; knock).
Corny (adj.) - old-fashioned, stale.
Creeps out like the shadow (v.) - "comes on," but in smooth, suave, sophisticated manner.
Crumb crushers (n.) - teeth.
Cubby (n.) - room, flat, home.
Cups (n.) - sleep. Ex., "I gotta catch some cups."
Cut out (v.) - to leave, to depart. Ex., "It's time to cut out"; "I cut out from the joint in early bright."
Cut rate (n.) - a low, cheap person. Ex., "Don't play me cut rate, Jack!"
Dicty (adj.) - high-class, nifty, smart.
Dig (v.) - (1) meet. Ex., "I'll plant you now and dig you later." (2) look, see. Ex., "Dig the chick on your left duke." (3) comprehend, understand. Ex., "Do you dig this jive?"
Dim (n.) - evening.
Dime note (n.) - ten-dollar bill.
Doghouse (n.) - bass fiddle.

More coming soon!