Among the strengths of the typing is its immunity to burn and poison. This obviously makes it very effective at combatting defensive teams, and I would be unwilling to see too many bulky Pokemon among its checks and counters. Below is a list of Pokemon I believe CaP3 specifically should and should not be checked by.
Dugtrio should be a check:
While I wouldn't call it a counter, as it will have difficulty coming in on any fire move of moderate power, CaP3 shouldn't have anything more advanced than substitute and the shed shell item to combat it. This means that CaP3 will be reluctant to take up an offensive role, but keep it more in line with the strengths of the typing: abusing key resistances. If CaP3 is offensive, Dugtrio would prevent it from being overpowering, and require that its team remove it before it tries to sweep or revenge kill.
Tyranitar and Politoed should be checks:
I did not say counters. If CaP3 was hard countered by one or both of the Top 6 OU weather starters, it would be significantly harder for it to operate due to its Stealth Rock weakness. I think that CaP3 should have some way of making them wary or forced to adapt to it (Burn, Poison, Coverage, Sunny Day), but ultimately be forced to switch if one of them gets in. This prevents it from being nearly unviable when its stealth rock weakness is considered, but allows it to be defeated by top OU playstyles with proper prediction or preparation.
Offensive Water, Rock, and Ground types should be checks or counters:
I'm looking at Starmie, Terrakion, Landorous, and to a lesser extent Gliscor here. The fact is, this typing does not lend itself to taking on the offensive playstyles in OU at all, and its strength lies in crippling the more defensive Pokemon on the opposing team to allow sweepers to set up. For instance, this typing allows it to destroy steels, absorb toxic spikes, and wall a few major OU threats with its typing. The weaknesses of it to offense are hard to redeem, and will probably end in creating a CaP that focuses on removing the weaknesses of a type instead of proving why it is good. While giving it an ability to deal with offensive waters would be cool, but ultimately it results in a Pokemon that is meant to patch up the weaknesses of Fire/Poison, instead of playing to the inherent strenghts of the typing. Therefore, I would have no problem with offensive weather sweepers, such as the ones outlined above, having a field day with CaP3.
Tentacruel, Jellicent, and Gliscor should not be counters.
This is where I will disagree with a lot of people. CaP3's typing is primarily meant to act as a defensive pivot, and give it a number of opportunities to switch in on steel-types, or Pokemon attempting to spread status. Given that the typing is so weak to many offensive threats, it almost needs to be able to break down the walls that would stop it, as it will be incredibly easy to revenge kill given the prevalence of Earthquake, Stone Edge, and water moves in the OU metagame. These three Pokemon not acting as checks would allow CaP3 to work as an excellent wallbreaker and/or stallbreaker- the natural strengths of its typing.
In a similar vein, defensive Heatran without Earth Power should be a basic stalemate, and Heatran with EP are probably an offensive Pokemon, and not worth checking. The same situation arises with CaP3 and Hidden Power Ground/some weak ground move designed to deal with Heatran and CaP3 while wasting a valuable moveslot.
There are a few other points, but most of them have been repeated. Alakazam should be a good revenge killer for this, which is basically inevitable. The same goes for Reuniclus, but it will probably be more of a counter. Conkeldurr is notable for not caring about the risk of status from burn or poison (either the status moves or its STAB move's effect chances) and be able to hit back with Stone Edge. Most fighting types will give this trouble, bar Virizion, Breloom, and Toxicroak.
tl;dr saying that "This should be able to cover for a water weakness" is trying to fix the type, and not show how it can be good, and there are other ways to play to the typing's strengths.