Not exactly. Where they're touch attacks a conductive weapon can help though, or the domain strike feat. If there are any which are SLAs then there's a feat which can quicken them. What did you have in mind exactly?
There's nothing like the paladin LoH, but this might work.
1. Get the domain strike feat.
2. Punch yourself as part of a full attack.
3. Spend a swift action to apply your domain power to yourself.
4. Spend the rest of your full attack on the enemy.
Be warned that your GM might just say No to this if you're not in the peculiar environment of PFS.
The only way to increase uses I can think of are some racial alternate favored class bonuses. Or raising your wisdom permanently of course.
In theory, the feat "Quicken Spell like ability" should work but you have to be at least 10th level before you can take it. Alternatively you could ask if you can take a feat that acts like Quicken Blessing but for your domain abilities. The 2nd option is both better and worse since you'll have to expend 2 uses in order to activate your domain ability (similar to quicken channel), but with enough uses you can do it more than just 3 times per day.
As specified above, when it comes to additional uses per day, if you are a dwarf, elf, half-orc or halfling you can get 1/2 an extra use per day per level as your favored class bonus. Otherwise, since it's based on wisdom anything that boosts your wisdom for 24 hours or more will also give you more uses per day.
While slightly off track but still in line with speeding up domain power activation, is there a way to make your self count as a higher level for domains so one could gain the lvl6-8 domain power early?
Everything that raises your level for domain powers that I can think of includes a phrase like 'This does not allow her to gain domain-granted powers earlier than normal.'