Bike is back firing and black smoke is comming out of pipes on indle. It has Cobra speedsters exhaust system.

Please contact the manufacturer of the exhaust system for assistance.

The carbs are running lean you need to richen them up and your back firing will stop.

if the o2 sensor is still in the pipes , it is ok
if not have the adaptor fitted to the pipes and it will be ok
the sensor reports the gas composition to the ECM to adjust the air/fuel mixture
if the new pipes are pollution control compliant the adaptor should be already there
if they are not then you are achieving nothing with the different pipes but are actually decreasing fuel economy

Yeah, with fuel injection, you need to either take it to the dealership so they can plug in and reprogram the ECM, or get a "piggy-back" unit to adjust the mixture.
Some, like the Fuel Commander, have about 4 knobs that you need to adjust.
BUT, to do this right, you need some dyno time, though you can get close by ear/feel.

I prefer a unit like a Terry Components.
This one reads the O2 sensors, and self adjusts, even over time learning your riding style and adjusts accordingly.

Here's their website if you want to read up on them:

http://www.terrycomp.com/

You'll want to look for the proper one under the METRIC selection.

Just a hint, they're about $450, but I picked up a brand new one on Ebay for $125.

If it's running rich already, a bigger jet will just make it run even richer.

As far as the rear cylinder running hotter, that's just the nature of the beast with a V-Twin engine, because the front cylinder blocks the airflow to the rear.

It seems there is too much of fuel going into the non firing cylinder thus the blackish spark plug, recheck the float level to that carburater and also check the valve clearance.

Might be your miracle in a can fix burning causing the smoke. If its coming out of a joint where it clamps, try to tighten the clamp. Sometimes there is also an exhaust gasket where the one pipe slips into the other pipe that could be broke or missing.

You may have to have it readjusted or re jetted if you change the amount of back pressure the engine gets from the exhaust. You will know right away if you get it started. It will act doggy and possibly foul the plugs.

check valve cover is it leaking oil. clean up the engine real good....i use chemtool B-12 carb cleaner.. wear gloves and don't breathe the fumes and if it gets on the exhaust, you"ll see smoke come off the pipes, so let it dry up before riding and wipe the exhaust pipes real good...now ride the bike and see if you see any smoke...when you do, pull over and take a look to see where its coming from...it could also be coming from a leaking exhaust pipe gasket.

Im not very familiar with your specific bike, but I do know what your problem is.cobra pipes are usually a straight-through design, meaning they have no muffler. the ones that do have a muffler usually have a very small one. smaller mufflers mean less fiberglass packing inside to absorb all of that noise. if your not too concerned about performance, then your best bet would be to go back to a factory exhaust. thats going to be the quietest one that you can use. Im sure there are also aftermarket systems available that also use a good muffler for noise control, but pretty much any aftermarket pipe is going to be louder then the factory setup. they are designed to give your engine more performance, which means less restriction for the xhaust gasses, which also means more noise due to the more open design of the pipes. Im not sure if your bike comes carbureted or fuel injected, but keep in ind that any exhaust changes made to a carbureted engine will require carburetor jetting adjustments to compensate for the change in exhaust flow. now, if you decide that your willing to lose just a tiny bit of performance for a quieter ride, then you may be able to find a used stock system on ebay for a very reasonable price. or if you want to stay aftermarket, then most companies test the sound levels of their exhaust pipes. by contacting the manufacturers, you should be able to obtain and compare the sound decible levels for different exhaust companies to find one that meets your needs.