Hi Javier,
KOY/S in the JAP engine number translates to:
K = 85.7 x 85mm bore x stroke (500cc)
O = overhead valves
Y = twin exhaust port
S = 1929
The J after the number means "roller-type cam levers and exhaust valve lifter".
The numbers on the face of the drive-side crankcase (50K...) have been added by someone - I think not Coventry Eagle.
So the engine is a typical sporty JAP single of 1929. The very rare racing engines have "R" in the prefix (e.g. KORY).
The gearbox is a 3-speed Sturmey Archer, pretty much a "Type MA" - a modified LS box usually supplied to Raleigh, but also used by Coventry Eagle in their new frame in 1929. The cast number "LS312" is the part number for the shell, and with the stamping WB2 is probably Sturmey Archer code for "LS supplied to Coventry Eagle in 1929". (I have a copy of the list of codes for 1932, but not for 1929.) The stamped number LS4622H is the actual gearbox number, and is pretty good for a type MA around 1928-29. "H" possibly means heavy gears?
The bike looks lovely! It has quite a number of modifications: rear suspension, mufflers, headlamp, carburettor... but I think you could leave them as they are - part of the history of the bike. The tank could be repainted in the 1929 Coventry Eagle colours of red, cream and black.
The Vintage Motor Cycle Club in the UK has a series of "Marque Experts" for the major brands: the Coventry Eagle expert should know all there is to know about your bike. If you email the VMCC with the details of your bikes (engine, gearbox, frame numbers, and a couple of photos) they should be able to forward the info on to the Coventry Eagle Expert who may help.
Cheers
Leon