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I'm playing a level 8 fighter with the archetype trench fighter and using the feat Sword and Pistol. When using feats like Power Attack and Deadly Aim I take around a -7 penalty on all attack rolls.
What magic items and weapon special abilities will lessen these penalties?
Beyond the typical items (e.g. those that grant a character enhancement bonuses to ability scores, weapons with enhancement bonuses), not much improves a sword-and-pistol-equipped fighter's ability to land attacks. I'm aware of only this:
once per round, when attacking with an off-handed weapon, the wearer can reduce any penalties on attack rolls made with that weapon by 2.
As an aside, I urge you to look again at your character sheet and confirm you aren't accidentally double-counting penalties. The penalties from the feats Deadly Aim and Power Attack don't both affect all attacks, instead separately penalizing, respectively, ranged and melee attacks.1
1 The penalties for wielding a 1-handed weapon in the main hand (some sort of pistol) and a light weapon in the off-hand (Kolman preferred the boarding axe as he was of river pirate stock) should be -5 on attack rolls with each weapon, even when combined with the feats Deadly Aim and Power Attack. Your character may be using 2 one-handed weapons, though.
There are lots of options in Pathfinder which trade accuracy (attack bonus) for various things (usually damage). You're using three of them here, which means you're choosing to give up a lot of accuracy. There's not much which is designed to negate the penalties, because otherwise they'd go from being tradeoffs to no-brainers.
Your best bet is to just stack as many bonuses as you can, and then let your penalties reduce you from "I almost never miss" to "I can land hits", instead of reducing you from "I can land hits" to "I don't hit enough".
That said, here's some options:
There's no special weapon properties I know of that make you more likely to hit, except for bane against your chosen type. So, while it may be boring, having a +3 rapier will serve you better than a +1 flaming keen rapier, and probably even better than a +2 agile rapier (although that depends on your Str vs Dex scores and the AC of your target).
The Gloves of Dueling increase your fighter Weapon Training bonus by +2. That's +2 more attack and damage with each category you've chosen (one already, the second at 9th level).
The Duelist's Vambraces allow you to reduce the penalty to your offhand weapon by 2. They stack with the gloves, since they're a wrist slot item instead of a hand slot one. It doesn't affect your main hand, though.
The pistol already is attacking touch AC, so reducing your attack bonus isn't that bad. But the sword, not so much. Consider not using Power Attack until you've confirmed the foe's AC is low enough that you're likely to hit even with the penalty from it.
Also, from my understanding of Sword and Pistol, the main use is to allow the pistol to fire without provoking. As such, you just need to attack with the melee weapon, you don't really need to hit. Hitting is a nice bonus, but (like a Magus' spellstrike with arcane mark) the main point is to allow your other weapon to be better.
