To the best of my knowledge, there are currently three methods to gain Dex to damage on the off-hand weapon.
Use Agile weaponry
This +1 equivalent weapon enchantment from the PFS Field Guide does the trick without any issues for finesseable weapons. Benefiting from this enchantment requires Weapon Finesse. Though the bonus on the off-hand is still halved. Contrary to the other two options, this one also applies when throwing these weapons, since it doesn't mention melee damage rolls.
This feat from Advanced Class Origins works only with full-sized rapiers, which are not light weapons, meaning you are looking at a -4 penalty for two-weapon fighting. However, it does lack the clear dual-wielding clauses of similar feats such as Dervish Dance or Slashing Grace. Instead, it only mentions "wielding a rapier one-handed", which doesn't explicitly forbid TWF. Dex to damage is instead of Str to damage, so it follows the rules for halving on the off-hand.
Pathfinder Unchained's Unchained Rogue class is an upgrade to the regular Rogue in 90% of the cases. One of the best new class features is Finesse Training, which allows to choose a single finesseable weapon and use Dex instead of Str for the damage bonus at level 3.
As above, this damage bonus is halved for the off-hand (though it is also increased to 1.5x for two-handed finesseable weapons, such as this one).