EWork in Progress, and subject to change and more substantial descriptions:
120 HP / 70 Att / 89 Def / 85 SpAtt / 89 SpDef / 87 Spe
PT: 178.5181 - Excellent
ST: 177.3354 - Excellent
PS: 106.3100 - Above Average
SS: 133.4821 - Good
BSR: 328.1192 - Very Good
Yes, I know that this rides the BSR limit. However, I believe that every point, bar possibly some Special Attack, is necessary to accomplish the goals of this stat spread.
The basis of this stat spread is that it deals with Volt-turn exceptionally well. At the start, I was trying to calculate a number of calcuations against Bulky Waters, but eventually I realized that it was fairly hard to make a stat spread that does this in particular, and if we give it another ability that doesn't counteract water moves, then the spread will naturally encourage Dry Skin. Basically, I wished to find a niche that Dry Skin and the typing allow it to do, but would still allow it to work outside of rain.
Why Volt-turn? Simply put, this Pokemon resists U-turn, and is immune to Rotom-W's strongest STAB move. While it will not like switching, and is easily dealt with by the partners of Volt-turn, I felt as if this could at least be a major asset against Volt-turn given team support, and it could do this to an extent without a water-dampening ability, even if it won't like taking Hydro Pumps at all.
Speed was actually one of the last things I considered with this spread, but I feel like listing it first, as most people seem to care most about it. This Pokemon was deliberately given 85 speed to allow it to outspeed and harm Modest Specs Rotom-W before it switches, if CaP3 has max speed investment. This can be used to get off a Toxic, or just about anything, without having to wonder what he's going to switch to. It also helps confirm if the Rotom is carrying Specs or a Scarf. While this speed is quite high, and indeed above most of its checks, I would like to point out that it allows CaP3 to outspeed one of the fastest bulky waters (Rotom-W), and greatly aids in destroying Volt-turn. Even then, only Heatran and Tyranitar are really outspeeded, and due to this Pokemon's offenses, both are still very threatening.
I'm listing them both here, as they are fairly similar in purpose. I decided that I wanted to optimize the bulk to allow it to just get KO'd by its checks, but also to ensure that it can deal with Volt-turn very well. In short, I picked a spread that allows it to take a U-turn and a Volt-Switch from Adamant Choice Band Scizor and Modest Rotom-W and come out alive, twice. This assumes that it has to switch into Stealth Rock, and that Rain is up to activate Dry Skin. If there is no rain support, the same results can be achieved by keeping rocks off the field. The high HP was chosen because CaP3 benefits far more form high HP than high defenses. No leech seed user wants to switch into a Fire Type, and this gives it extra insurance against Blissey's and Chansey's Seismic Tosses. As for concerns about the relatively high bulk allowing CaP3 to survive its threats, this is not true. Assuming 252/252 physical defenses, not a single one of the ground or rock type threats listed, in addition to Earth Power Heatran, will fail to KO CaP3 if it switches into Stealth Rocks once. Only Gliscor really comes close, and Gliscor is probably the check CaP3 can do the least back to, due to its effective status immunity.
In general, high bulk allows this Pokemon to deal adaquaetly with Volt-turn, and encourages bulky boosting sets, or simple status-spreading sets, that work well with its impressive set of resistances.
I'll start with Attack. Engineer Pikachu made a very good argument for 71 attack earlier on the page, so I'll just summarize. This physical attack, while far from impressive, lets CaP3 deal with Virizion and the incredibly Specially Bulky waters more easily than it would with a very, very low attack stat, and makes Coil a viable boosting option. However, this set still fails to 2HKO almost any of its checks with just physical poison coverage.
Special Attack is a bit trickier. It took me a while to come up with 90, and I may still change it, but I'll just lay out the basic case. 85 base Special Attack, unboosted, allows CaP3 to 2HKO most Bulky Waters, often through leftovers. This includes Rotom-W, which is a pretty major focus of this particular spread. The exact number could be brought down a little bit, but I like it at 90 to keep CaP3 offensively workable, but not overwhelming by any standards. I'll have more calcs tomorrow. As for the bulky waters that CaP3 can't 2HKO, most are either threatened by Toxic or do roughly 20% back to CaP3, allowing it to use them as set-up-bait. Indeed, the only major failing of these offenses is that they don't threaten Tentacruel, but Tenta can do almost nothing back bar set up Toxic Spikes that CaP3 can absorb later, and Rapid Spin, which would be a problem bar Special Attack investment much higher than what anyone is seriously proposing.
tl;dr This spread allows CaP3 to deal well with Volt-turn as a cool niche granted by the typing and ability. The set is threatened by the Pokemon designed to threaten it, and has the bulk to capitalize on the resistances, status, and boosting moves granted by the typing.
Will edit in specific calculations tomorrow.
Edit: Random Calcs
LO Timid Starmie Psychic vs 0/0 CaP3: 85.03 - 100.78%
LO Timid Starmie Psychic vs 252/0 CaP3 : 72.97 - 86.48%
LO Timid Starmie Psychic vs 252/0 CaP3: 55.85 - 66.21%
CaP3 wtith max Special Defense investment can potentially survive hits from LO Starmie, although this still allows niche sets to beat it.
Timid Specs Toed Psychic vs 0/0 CaP3: 59.31 - 69.81%
Timid Specs Toed Psychic vs 252/0 CaP3: 50.9 - 59.9%
Timid Specs Toed Psychic vs 252/252 CaP3: 39.18 - 46.39%
Even Politoed carrying a move to get around one of their checks will still be poisoned by it. And this is assuming its most powerful set. Bulky Toed will have basically no way of getting around CaP3.
Timid Specs Rotom-W vs 252/128 CaP3: 31.98 - 37.83%
Adamant Choice Band Scizor vs 252/128 CaP3: 8.78 - 10.36%
Super Power isn't that much more impressive. Basically, my spread neuters Volt-turn due to its typing, ability, defenses, and speed stat. While Rotom-W with Pain Split is an issue, it doesn't like Toxic, can't do much back, and in the rain CaP3 is healing off the damage fairly easily. Consider that it's Volt-switch isn't doing much more.
Upon being asked to explain it, I prefer high HP and lower defenses, because I want this thing to beat the standard Special Walls, and believe that since this already matches up well with the top Pain Split user, that really only leaves Gengar in OU, who is not on our threatens or threatened list, and is a much smaller price to pay than the gains earned by letting this take on Chansey, a key member of rain stall, and win 1 vs 1.
Timid Specs Tornadus Hurricane vs 252/252 CaP3: 54.95 - 64.86%
It does not beat all of rain with my spread, and there are still many rain threats this can not beat.