How to replace 6V battery with capacitors
ADDED:

Information I gave below is good enough.
See circuit diagram added at end and reference to electrical manual.

Bike uses classic coil ignition with rectified alternator to battery.

Using a LARGE capacitor may work BUT you risk system damage as voltage may be able to go very high with not enough load - and may not run coils if too much load.Also, higher voltage cap is smaller electrically per size but lower voltage one risks being overvoltaged by system. You could try 50V electrolytic as large as you can find surplus. 16V is too likely to be damaged probably. 



My idea of an electronic clamp is an OK one BUT a low self discharge battery is a better idea still (or a solar charger or some other trickle charger).

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You need to get a good feel for what the system does with the 6V. What brand and model of motorcycle is it? It is quite possible that you do not need the 6V at all for the ignition - but you may have already found that you do. 

If the 6V is only for the headlight and you have eg magneto or fully self powered electronic  ignition then the headlight can probably be powered with no battery BUT you MUST clamp the voltage to stop it going too high - too high and bulb will blow (ask me how I know :-) *).. A clamp can be a bridge rectifier and a MOSFET which applies a large Wattage resistor when voltage gets too high - or even a short circuit is OK in many systms. Regulator bang/bang regulates.

The energy requirements of a spark ignition system are liable to make a capacitor solution unattractive. 

Thinking laterally, you could consider using.


Eneloop NimH batteries (new style) which give you years of self discharge time.
18650 LiIon x 2. - stripped out of old dead laptop packs. Often some cells are still good. Charger can be a voltage clamp that ensures voltage for two cells in series does not get above say 7.5V. A zener would be sharp enough for this in this application. 
Small PV (solar) panel to charge battery or keep charged when not in use.
(depends on where bike is stored. 





Long ago. TS90 Suzuki. Convert electrics to 12v. Add halogen headlight . Marvellous. DO NOT miss gear changes at night !!!.
Gravel road, 24 hour road trial, middle of night, fun!. Corner, change down, whoops - miss gear change, bright, brighter, brighter still, Black. Soon a Honda 750 cometh. We dance together over many gravel miles, I riding as best one may on his headlight beam. Quite a journey. 




CB125 wiring diagram

You can download a SLIGHTLY better quality version of the file below from my drobox here - the version below when copied an compared has more jpg artefacs.
 My version is a sligtly tidied up version of one I found here
 Which was from ths utterlu superb collection of Hinda wiring diagrams - 120+ all free to download.





Rather good CB125 electrical manual -from the days when Honda didn't quite do English proper but put in far more technical material than you'd get nowadays.    

Version on my dropbox account which I have unzipped
 or
  Zip version on a suspect looking website that actually did work OK not a site I'd frequent if possible.