The Sport, like the Paso, came with a 2 barrel Weber carb adapted from an automotive application (1200cc Fiat?). Needless to say, it had some issues. It was a good idea, it was just implemented badly. Further proof that the Sport was a parts bin bike and the development team had no time to finish complex problems like proper carburation.
The biggest problem was that the fuel pump was too strong for the needle jet in the carb, thereby flooding it, all the time. Putting in a pressure regulator at 3psi improved things imensely. There were a few other tweaks you could make to get the stock carb working reasonably, but 'reasonably' was all you could expect. There was a whole lot more potential in the engine if you change out the carbs.
In the Paso, you could bypass the fuel pump, but you can't do that in the Sport. The fuel lines in the tank are brazed in such a way that if you take out the fuel pump, you will only use 1/2 of the tank's capacity. Not a good option. Make sure your fuel lines have a T in them that returns to the tank. This keeps your fuel pressure reasonably low and won't flood your carbs. The return line is one of the stubs in the middle of the tank. One is a vent, the other is a return.
The first aftermarket carbs that were available were the 36mm Dellorto carbs with either the Mallossi short manifolds, or some from a Pantah (grab the whole setup if you can). You need to get a duel cable throttle twist grip. The Tommaselli Daytona 2S it the best choice (probably the only choice). The 36mm carbs work the best on the street. The old F1 had 40s on it, which made it a dog on the street, but good on the track. Don't be tempted to put the 40s on, it won't be an improvement from the 2 barrel Webber. They are way too big and you wont like you bike. (good for a 900 though)
I've been sneaking up on the jetting on my 1990 Sport.
Current jetting in my 36 PHM Dellortoswith 2into1 exhaust
160/162 main (richer in back)
K5 needle in middle postion
Some others are running a 261 atomizer, also known as the needle jet or needle seat, They also run a bit fatter needle, like a K27. For some reason, The jetting I have seen posted are all over the place. Some people are running a 135 main, which my bike ran horribly on.
The intakes for the carbs get awfully close to the rear cylinder, and the battery. Air cleaners just don't fit well. I put the Dellorto grey plastic screw on bells (velocity stacks, intake runners, whatever you know them as), and attached 2" rubber elbows that allowed me to put some UNI air filters sticking straight up into the area where the stock airbox used to be.I bought them from http://airflowonline.com/
, the part number is 90HL2 Rubber Intake Hose 90 Degree 2" less than $10 each.
Adding a bit of length between the air cleaner and the carb vastly improves low end performance and torque. There's a phenomenon called fuel fog that comes back out of your carb at lower rpms. If you don't contain it, it becomes a variable mix, sometime too lean, and sometimes too rich. There's also the complex topic of laminar flow and Helmoltz resonator. Without getting into complex intake design and fluid dynamics, trust that adding just a few inches of intake trakt will make the bike run much better, all the way across the range. This is one of the functions of a stock airbox. Race bikes historically didn't use an airbox because they are rarely using the low end, but a street bike does all the time. If you run straight air filters, try and stuff the longest velocity stacks into it that you can fit. ( I just read that one of the big changes to Casey Stoners bike this year is a new airbox to improve midrange)
The other popular carb swap, and much cheaper, is to grab a used set of stock carbs from the Monster or SS line (91-98) They are Mikunis, and are tied together, so you keep your single cable throttle. Make sure you get the intake manifolds to go along with it. If you grab some from a 900, it will pretty much run straight away. The 750 carb set, while basically the same, will need a bit of jetting change to get it work at its best. On the Sport, this carb system is aimed right at the battery, so air cleaner options become a bit limited. Someone posted a picture using the plastic plumbing of a J-Trap, which I thought was rather creative. I haven't heard of anyone adapting a stock airbox to the Sport, but if you have the time and parts, we would all love to know how that works.
The high performance option is the flat slide Keihin FCR carbs. Since they are the popular option for the SS and Monster, they are in demand and you won't find them cheap. They will run almost $1k new, but you will find a lot of people who know how to set them up and will be able to help you get them jetted correctly. Its also the easiest option to buy new, and get what you want. Again, air cleaner options become limited, and you need to become creative. This is the best option if you have the money.