Smogon has an useful thread about BW2 in-viability rankings, which are helpful to decide what Pokemon you should use. Azurill is ranked A- and is the highest ranked water-type in the viability rankings.
Availability: Early Game, Floccesy Ranch, 20% (Azurill) - Mid Game, Route 6, 5% (Marill)
Stats: Only really lacking in Speed, but Azumarill is both bulky and packs a real punch when using Huge Power. It has essentially 150 Base Attack.
Typing: Water is a great typing both offensively and defensively. Water STAB in general is a huge asset and there are no principle Grass- and Electric-type trainers to worry about.
Movepool: Azurill gets access to Frustration as soon as it is obtained, and then Return immediately after the first gym. This goes well with its Normal typing and its evolution type. After that, Azumarill gets Aqua Tail at level 21, and then access to Waterfall and Superpower, as well as Ice Punch through tutoring.
Major Battles: It has uses against most of the gyms, just through sheer strength. Clay should prove no obstacle, and you can even smash through Drayden's Dragons. Against the Elite Four it is a similar story, just by using sheer strength. With Ice Punch you can take on Iris in a similar fashion, taking hits and firing back with super effective moves.
Additional Comments: Only use Huge Power. The other abilities will not help you at all. All you need is to take advantage of that wonderful Attack.
If you don't mind low speed, then this is your best choice. It has a chance of being Huge Power, having great attack stats as well as decent bulk. Only what it lacks is speed, but that's make-up by its good bulk as well as decent move-pool. It gets Aqua Tail by level up, as well as Waterfall via HM. In Driftveil city, you can teach it Ice Punch at the cost of 10 Red Shards after which it starts dominating and punching Drayden as well as Iris. If you still think speed is superior over bulk, there are some other options apart from this:
Availability: Mid Game, Route 6, 70% (Surf)
Stats: Basculin has good Speed and offensive stats, allowing it to be a decent mixed attacker. Its defenses are poor, however.
Typing: Water is a good offensive and defensive type. There are plenty of regular trainers with Water-weak Pokemon out there, though it isn't as useful against stronger trainers.
Movepool: Basculin starts with Surf, and it learns Aqua Tail fairly early. Combine that with Adaptability and you have a Pokemon capable of 1-2HKOing most Pokemon you encounter effortlessly. Basculin also gets Blizzard/Ice Beam, Double-Edge, and Crunch, but it will be using its STAB moves most of the time.
Major Battles: Unfortunately, Water isn't particularly helpful against the last Gym Leaders. Basculin's better match-ups are against Shauntal and Grimsley since both carry Water-weak and/or frail Pokemon on their teams. It can also take down Iris's Archeops and Aggron.
Additional Comments: You should always use Adaptabilty on Basculin because it provides it with impressive sweeping potential against regular trainers.
Here are sets for both:
Azumarill @ Nothing / Mystic Water
Ability: Huge Power
- Return (TM from 1st gym) -> Dive (HM)
- Aqua Tail (Lvl 21) -> Waterfall (HM)
- Superpower (Lvl 42)
- Ice Punch (Driftveil City move tutor, 10 Red Shards)
Basculin @ Nothing / Mystic Water
- Surf / Aqua Tail
- Ice Beam
- Dive / Double Edge
Hope this helps!