Any game ive played if you wanna beat a sniper, first it depends how good the sniper is, if they're really good and you aren't, chances are they'll get you so it might be best to just avoid them unless you dont care about dying.
Most of the games i've been good at are close up games, like halo, unreal, gears, cod (Yes i know not all maps are small, but for the most part...) so I was never really up against a true sniper who would hide take his shot and swap location. It was mostly a talented shooter who could take your face off up close just as well as he could at a distance (By the way im not sixist lol, just all the tournament players i knew were male, there were a few girls who came to watch but they were awful
). From what ive seen of Brink, its obvious a sniper is going to be more of the type I faced, than the long range hidey hidey movey movey type.
In which case I dont think you can have a set tactic for taking one out as it depends on which location on the map you bump into them on. If they are holding down one of the long range areas we have seen in videos e.g http://www.youtube.com/user/BrinkVideos#p/u/0/l_CykYOy6Lw, then it depends what weapon you have, if you have a rifle as well then you want to basically try an out shoot them, you have the advantage of knowing where they are and the abilitiy to pop out from different areas, in the end though it comes down to your individual skill with the weapon. If you dont have a rifle that can accurately hit them at that range then you will want to close the gap otherwise they are just gonna keep putting accurate shots down on you. Closing the gap can be done in any number of ways, fire at them and start running hoping they duck, if your teamwork is good enough then get someone else to put them under fire while you move towards them (personally i think this one is slightly unrealistic, im not saying it wont work, but you have to remember its not just a battle between you, your friend and the enemy sniper. He has 7 allies most likely nearby thus making it very hard to focus this considerable level of teamwork on 1 person). If you're a spy then disguise and make your way to them or you could always just trust in your skill in movement, make darting runs from cover to cover or just move towards them strafing, sliding, bouncing and sprinting as you go.
If you find yourself in a bottleneck situation, trying to fight through enemy lines to an objective and they have a person equipped with a rifle doing heavy damage from the back to anyone coming through the gap, then frankly you are in trouble. Firstly you want people to stay trading fire through the gap so the enemy doesnt push out, meanwhile you want people trying to enter via an alternate route. If there is no alternate route, which I highly doubt, then its just a case of shooting better than the other team, get grenades in there and keep pushing through. In this case, the sniper guy at the back should be the last person you focus on really as you want to kill the people nearest the gap so your team can squeeze through. Although if you wanted and you had a good line of sight then it wouldn't be a waste of time to get some rifle shots on their sniper as well.
Sorry I went off on a bit of a waffle there :/