One of things about using clerics without Spell Lists is that it fits well with Scott Ludwig's Basic D&D Custom Class Template. Since the ACKS custom system is really similar, once I get the Player's Companion, I can make comparisons.
The system uses thirds and halves, so custom classes are easy. 1/3 Cleric gets two categories, 2/3 Cleric gets four, 150% gets 8 categories.
For the Human Template, anyone choosing 200% for Divine gets all 11. I would like to have 12, but even one of my five additional categories is a bit of a stretch.
Looking at the sample Paladin at the link: d6 Hit Dice, three categories, melee weapons as "Monster" and missile weapons as a Magic-User. I like the idea that not all Paladins are the same.
Will a 1/2 Cleric get a category at half strength? That's up to you. It complicates the formulas used to determine success. Since it's a custom class, though, you can just make a table for success.
If you go the full strength route like me, I simply changed the XP values for Divine. Basically, it matches the Arcane table. This breaks the system for calculating a regular Cleric, but since I allow a spell at 1st level, I use a different chart for Clerics anyway.
One other route could be to have a Piety score. By default it could be Level/3 for non-Clerics and set a Hit Dice limit on using the categories. This means a Paladin with Healing is not healing 2d6 hit points until 6th level and reaches a ceiling of 5d6 at 15th level. The other advantage of going this route is that you don't have to say "no spells at 1st level", the only category that can be used at 1/3 power is healing and that only equates to 1 or 2 hit points.
Still some details to work out. The Paladin still feels too powerful even with my change to the XP Table. (Which is 2125 XP to advance to 2nd level on my adjusted charts instead of 1750 xp on the standard chart.) Also, changing the Divine chart has consequences for non-human clerics.
Here is the conversion of the Turning Formula for ACKS:
1d20 + ( 3 * (level of cleric - hit dice of undead) )
Hit dice of undead is increased by one for every special ability (asterisk next to HD number)
Success is adjusted roll of 10 or better
For example, 1st level cleric turning skeletons:
1d20 + (3 * (1 - 1) ) or roll 1d20 with a 10 or better.
As Keith Davies mentioned in the original G+ post, there's a better way to state it:
d20 + 3*level >= 10 + 3* (undead HD + special)