From my experience, piety does NOT increase DoT damage at all. I tested it in a manner I feel was rather thorough. First off, I tested it on the level 3 marmots with 50 piety, and it took 11 ticks to kill it, with the last tick being overkill. It was doing exactly 75 damage per tick. I killed the same monster 4 more times for a total of 5 kills, all of which produced the same results, 11 ticks of 75 until the monster died. I then boosted my Piety to 120 and tried again on 5 more marmots, exactly the same result; 11 ticks of 75 damage.
To conclude the test, I went out to kill Dwarf Diremites, the level 45 ones. It took 29 ticks at 50 piety with Poison II to kill one, and the results were identical for 11 out of 11 kills. That equates to 75 damage a tick, once again, as the last tick was quite a bit of overkill. I then reallotted my points to 120 piety, and killed 4 more. They all took 29 ticks of Poison II to kill. Thus, I'm pretty certain piety does not effect damage over time damage at all, it only effects the likelihood that they will stick, and the duration the effect will remain active for. I intend to test INT when the servers come back up, as well as magic potency to see if either of them makes a difference, but I am doubtful, as I alternated between different weapon types and armor during the entire process.
Edit: Oh, I wanted to mention one other thing... I believe Piety probably works in a similar fashion that certain stats in FF11 worked. There is most likely a cap at which it will be beneficial to you, because the check the game performs is your piety vs the target's piety. Piety also governs your chance to resist a spell, mind simply boosts the magic defense (meaning mind makes you take less spell damage, while piety allows you to completely avoid it). After your piety exceeds a certain number above what your particular target's piety is at, it is most likely useless.