The Rainmaker is a pretty good weapon for Rainmaker. You need it to win, and theinknadoes it shoots are pretty large, fairly tall and cover a large amount of turf with each shot. Yeah, it slows you down, only the fully-charged shots are worth anything 90% of the time and you die automatically after holding it for a while (shorter time if you run toward your base), but it's still fairly useful, which is good, since moving it forward is the only way you can win.
But as for weapons that aren't one of a kind, I have a few thoughts (WARNING: VERY LONG, THERE WILL BE A TLDR AT THE BOTTOM OF THIS POST):
1) Anything with a Sprinkler is good. You can ink an area passively with it, but the best thing about bringing a Sprinkler to a Rainmaker match is that you can put it next to the Rainmaker's shield and it'll ink the shield from inside the shield, becoming practically unassailable and making the shieldsplosion more likely to be in your team's ink.
For a few weapons that have Sprinklers, the .96 Gal has great range and power, and Echolocator to avert ambushes and track the enemy-controlled Rainmaker while they're swimming (which, at least on my minimap, makes them invisible on the minimap), though it does fire a bit slowly so you're vulnerable to ambushes and its ink efficiency sucks. The Kelp Splat Charger/Splatterscope is better from a distance, but a careful throw can place it from not-point-blank (too close and your Sprinkler gets destroyed by the shield, too far and it might not get under the shield), and you can deal high damage per shot to the shield with charged shots, or just pop it with the Killer Wail, and you can snipe enemy Rainmaker carriers or ambushers going after your team's carrier from a distance, though you're probably screwed if attacked up close. Finally (not going to cover every weapon that fits each example, just two or three, makes this shorter), the Inkbrush can speed up to the Rainmaker and drop a Sprinkler right in front of the shield (or drop an Inkstrike on it to pretty much guarantee its explosion is your color), then pick it up yourself or ink a path for whoever does, though unless you're great at ambushing you want to run away from combat (except the Rainmaker, which charges slowly enough that you can probably trade at worst).
2) Splash Walls are generally good in this mode. You can use them to block Rainmaker shots while you splat them, or putting up in front of your Rainmaker carrier so they can charge shots safely for a few seconds.
For a few weapons that have Walls, the .52 Gal has great power and respectable range and speed, and Killer Wails to pop the Rainmaker from anywhere, though you can be outranged so look out for that. The .96 Gal Deco has awesome power and range and the Kraken for annihilating the Rainmaker carrier or inking a path for them while invincible (and it pops the Rainmaker in about 3ish hits on its own, which is nice), though your fire rate is pretty slow so ambushers will probably splat you and your accuracy at long range is not that great (at least in my experience) and you're slowed to a crawl while firing, so not very mobile, also your ink efficiency still sucks. The Jet Squelcher has the longest range of any shooter-type weapon and decent power (3-shot before Defense Ups) and an okayish fire rate (still should worry about ambushers, but you're not the .96 Gal), and Inkstrikes are good for covering an area and popping the Rainmaker, though your fire rate isn't great. Finally, the Heavy Splatling has an amazing fire rate, great range and has Inkstrikes for insta-popping the shield, though your wind-up time is a liability and your shots are kinda weak.
3) Anything with Killer Wail/Inkstrike can pop the Rainmaker's shield from anywhere, which is certainly decently useful.
For a couple of weapons with Killer Wail, the L3 Nozzlenose has an amazing fire rate, good range and barely slows you down at all while firing (not that it matters, given it's a quick-burst-fire weapon) and has Disruptors to slow the Rainmaker carrier or potential carrier-ambushers so you can splat them (or a teammate can) easily, though it takes some getting used to the burst-fire-ing, and you need at least 4 shots for a splat, and each burst has 3 shots so you need to fire two bursts minimum for a splat. Also, the Blaster is similar to the L3, but instead of 3-round burst-fire, you shoot a single shot that explodes, splatting enemies on a direct hit (or a couple of near-misses), but slows you much more while firing, leaving you very vulnerable if you miss, and the explosion probably won't affect close-up enemies (unless you get a direct hit, then you win).
For a couple of weapons with Inkstrike, the Splattershot Pro has good range and respectable power and speed, plus Splat Bombs for attacking farther-off foes (or over walls), though its ink efficiency is bad. Also, the Gold Dynamo Roller has very wide, decent-ranged and very powerful swings to assault the Rainmaker's carrier and anyone guarding them, and also has Splat Bombs for longer-ranged attacks, though its swings are rather slow and its ink efficiency isn't good.
4) The Kraken is surprisingly useful here, since it can be used to smash the Rainmaker's carrier easily since they're slowed and can't run away as easily, and you can use it to ink a path for your Rainmaker carrier.
For a few weapons that can release the Kraken, the Octobrush is very fast, has wide, fairly quick and decently powerful (3-shot before Defense Ups) swings for attacking grouped enemies or the Rainmaker carrier, and has Squid Beakons to let teammates more quickly reach areas for flanking or just escaping from danger, though its range isn't that great and its ink efficiency is only okay (it's no Splattershot Pro, but it's no Splattershot Jr. either). The Custom Jet Squelcher has its regular counterparts great range and decent power (but slowish fire rate), but trades in Inkstrikes for the Kraken and Splash Walls for Burst Bombs, which can soften up foes so you can splat them in fewer shots, though it lacks the defensive measure that Splash Walls provided and still has a slowish fire rate. Finally, the Custom E-Liter 3K has the second-longest range in the game (second only to the E-Liter 3K Scope) and has Squid Beakons to return to your sniper nests when splatted, though its slow charge means you'll get splatted by most ambushers or anyone who gets close enough to fire at you for a second and being far away from the action is not the best place to release the Kraken (but if they get close to you, Kraken away).
Generally, anything with one of those things listed above is at least usable, though those aren't required for success. And I could be wrong about some or all of these, so take them with a grain of salt.
TLDR: Any weapon with Sprinklers, Killer Wails and/or Inkstrikes can easily pop the Rainmaker for your team, any weapons with Splash Walls are good defensive options for attacking the Rainmaker carrier from relative safety or letting your team's Rainmaker carrier charge a shot or two safely, any weapons with Kraken can easily dispatch the enemy team's Rainmaker carrier or unaware attackers against your team's carrier.
Weapons without these can be great too, and weapons with these aren't guaranteed to be great (for example, the Inkbrush has Sprinkler and Inkstrike, but I wouldn't recommend it over the N-Zap '89, which has that and better range), but they're good options to have for Rainmaker, so picking weapons that have them is probably a good strategy.
But like I said, I could be wrong.