When using a rain team, you need to be 99.9% sure that you'll set up the rain every time, or you're just using a bunch of Pokemon with shared weaknesses and similar type coverage for no reason. Ludicolo and Toxicroak are typically used together, and for good reason: Ludicolo has pretty good bulk, can set up the rain, and can outspeed almost everything and smash face with Surf once the rain is set up, while Toxicroak can use Fake Out to flinch anything that might be threatening to Ludicolo (except Inner Focus users).
People don't just use OU Pokemon like Zapdos and Kingdra on rain teams because of their high base stat totals; they provide valuable resistances to the other members' common weaknesses, and they have enough bulk to switch in when they need to. Kabutops is the weak link here; the biggest reason to use rain teams is the ridiculous sweeping power of using two rain-boosted Surfs at once (or smashing your opponents with Surf while healing your own Water Absorb Pokemon), and Kabutops's poor bulk and unreliable secondary STAB don't make up for its inability to help that strategy. I'm not sure what to recommend if you're refusing to use Starmie, Suicune, Zapdos, Kingdra, and Empoleon; you could use Gorebyss for its power, but it only has a 2x resistance to Water (meaning you'll often kill it with Ludicolo's Surf; it's pretty poor in terms of Special Defense) and its pure-Water typing doesn't really provide much to your two leads, even if it does more than Kabutops' Water/Rock. As insane as it sounds, Lapras could work; it has decent bulk (ignoring its Rock and Fighting weaknesses, but the BL restriction doesn't offer much that resists those while making good use of the rain), has Water Absorb, and can make good use of Surf, Thunder, and Ice Beam. Of course, it's very slow, but you take what you can get. That gets rid of one of your Ground weaknesses, and without being able to use Zapdos (whose Ground immunity is one of its main selling points on Rain teams), that's about the best I can come up with. You'll appreciate Ludicolo's Ground resistance, at least, and hopefully you'll outspeed and quickly KO most Earthquake users.