The gsxr 600 fuel injected engine in my single seater is running rich, puffs out black smoke when you rev it, even after it is warmed up.
When it idles, it is very lumpy like a car engine with the choke out.
I just wondered if anybody has any suggestions how to adjust the fuelling, if it can be.

Are you sure it's just the tune that needs adjusting? If it was running OK previously it sounds more likely one of the sensors or wires has failed giving the ECU the impression it's not warming up, so it's running rich to compensate, or something like that.

Has it started doing this, or always done this?

If its the former then I'm with FBB. It surely must be a sensor, I think water is likely. Alternatively it could the TPS has got rotated around a bit, which might have a similar effect.

Sensors......

Vacuum manifold depression is a good candidate, is it still connected. It'll be a small rectangular black box thing (green or pink label depending on vintage) off the throttle body array. It's partner will be somewhere too, with an open end (atmospheric). If these are not OK< you'll get rich, sooty 'running'.
Other than that, it's something else the ECU needs, as mentioned previously.

Plug in the instruments and get an error code, I'll tell you what's wrong if you don't have a manual to hand (it's sad that the codes are burnt into my subconscious).

Thanks guys, sadly I'm off to work now, yes some of us work on Sundays, but will have a look when I get back.
Cheers