The Fighting type is a great addition to this Pokemon in that giving Sun a boost against Sand may not do much to help out Sun if it only forces Rain users to switch to Sand. The type I would like to see discussed is Grass/Fighting.
Grass/Fighting has a few bonuses to it that help it dump Rain, help itself against Sand, and most importantly, benefit Sun. The qualities I see in Grass/Fighting are as follows (pwnemon I like your list idea so I will use it for my own purposes!):
1. Stealth Rock Resistance
Making this Pokemon resistant to Stealth Rock is going to strengthen this Pokemon's role as a defensive pivot if we choose to go that direction and give Sun something that both Sand and Rain have: a Stealth rock resistant tank. Sun teams naturally have plenty of Pokemon weak or neutral to Stealth Rock, so giving this Pokemon Grass/Fighting as a typing would ease the hazard burden that most Sun teams have.
2. Resistance to Water and Electric
Water and Electric are two types commonly used by Rain teams, specifically high-powered Special attack by Pokemon such as Thundurus-T, Keldeo, etc. Giving this Pokemon resistances to Water and Electric (and enough bulk to handle coverage moves) will let it better handle Rain teams. Pokemon like Keldeo can rip through Pokemon without Water Absorb, Dry Skin, Storm Drain, or a resisting type, so unless we stick on an ability that defeats Water-type Pokemon we will not be able to adequately handle the high-powered Water moves commonly seen on Rain teams. The Electric resistance provided by the Grass type allows our Pokemon to handle Thundurus-T, Jolteon, and Politoed's various Thunder buddies, strengthening this Pokemon's role as a Rain counter.
3. Can attack Water-type Pokemon right off the bat
Grass typing means Grass STAB. Being able to sponge a hit from something like Keldeo or Politoed doesn't mean much it we can't hit back with Giga Drain, Power Whip, Horn Leech (notice how many Grass STAB moves give this Pokemon semi-reliable recovery!), or whatever STAB Grass moves we decide to give this Pokemon. Furthermore, we would not need to bloat this Pokemon's attacking stats if we can just hit Water types super-effectively, so we can focus on giving this Pokemon the defensive stats to weather the rainstorm of OU. Though Jellicent isn't the spinblocking titan of OU, beating OU's bulkiest Ghost will clear the way for this Pokemon or a teammate to Spin away the hazards that hamper Sun's usefulness.
4. Increased potential for a Sun-benefiting ability
This is more of a flavor argument, but Grass types commonly have abilities like Chlorophyll, so giving this Pokemon a Grass typing will bring Chlorophyll into serious consideration for later. Excuse the minor polljump, but giving this Pokemon Chlorophyll creates the incentive to use this Pokemon on a Sun team.
5. Can beat Heatran if paired with Rotom-W
Though this typing fails to switch into Heatran at will, if we pair this Pokemon with Rotom-W or another slow U-Turner or Volt Switcher, we can take Heatran's attack and then retaliate with a Fighting-type attack to theoretically OHKO the Sun counter.
6. Beats Dugtrio barring the rare Aerial Ace
Resists Earthquake, resists Stone Edge, and has ways around Reversal (Leech Seed anyone?). Instead of living in fear of Dugtrio, Grass/Fighting would let CAP5 switch into Duggy with impunity unless Duggy decides to use Aerial Ace, which is a pretty rare move for Dugtrio since it kind of needs all four of its moveslots for Stealth Rock, Earthquake, Stone Edge, and Reversal.
7. Is not demolished by Sand.
The Fighting type gives this Pokemon a resistance to Stone Edge, Crunch, Pursuit, and Earthquake, the four most common moves on Tyranitar and Hippowdon. Super-effective coverage on those Pokemon and Terrakion (plus a neutral hit on Landorus) gives this Pokemon the ability to grapple with Sand just as well as it grapples with Rain. Common Sand abusers will not be able to break this Pokemon and thanks to the neutrality to U-Turn and resistance to Volt Switch, VoltTurn Sand teams will have just as much trouble.
8. Weaknesses are all covered by natural teammates or good defensive stats.
The most critical weaknesses of this type are Flying and Ice, but in reality, this is not a significant issue. The only common spammer of Flying moves outside of the rare Acrobatics Gliscor is Tornadus, who is both an uncommon presence in OU and is not a 100% counter to a Grass/Fighting CAP5. In Sun, Tornadus will only be able to hit CAP5 with Hurricane 50% of the time, so a Tornadus user will have to risk a 50/50 chance to kill this Pokemon with Hurricane or else switch out. Meanwhile, an Ice weakness is not the end of the world because most Ice moves in OU are coverage moves on Pokemon such as Starmie, Politoed, Landorus, Thundurus-Therian, etc. Giving this Pokemon adequate Special Defense would offset this Pokemon's Ice weakness. Look at Specially Defensive Celebi for example: Specially Defensive Celebi can take plenty of Hidden Power Ices or weak Ice Beams despite its weakness, so we are not necessarily screwed against Ice. The only common Ice Pokemon in OU, Mamoswine, is weak to both of this Pokemon's STAB types, so even the strongest Ice types in OU cannot defeat CAP5. Fire is another salient weakness on a Grass/Fighting CAP, but that's where this Pokemon's teammates come in. Sun teams commonly use three or four Fire resists per team, so it's not critical to resist Fire. Even if this Pokemon was neutral to Fire, the power of Sun would boost Fire moves to a point where it wouldn't really matter whether or not this Pokemon was weak to Fire.
9. Theoretically counters Ferrothorn
Leech Seed immunity, Grass resistance, and Fighting STAB. Knocking out Rain's best defensive pivot and half of its sweepers make this Pokemon Rain's bane. In conclusion, Grass/Fighting provides this Pokemon the tools necessary to boost Sun as a playstyle and severely hamper both of Sun's rival weathers.