One way to make the users of sacred magic feel like they are working with freely given miracles of faith is to keep the standard spell list and rules, but have casting in a short time frame (combat round) determined by a petitioning die roll. Here we are assuming that cleric spells are not memorized (cast at will) but that they use a system of levels and slots similar to magic spells. Roll d20 plus the caster's level minus twice the spell's level. On a modified roll of:
1 or less: The spell fails and the caster has spent both the spell's slot, and another of the same or higher level. If another is not available, the caster must atone by making a journey of 1 day/1000 of his or her xp, or a sacrifice of 1/10th xp in coins (or a being equal HD to level) before being able to call on sacred magic again.
2-4: The spell fails, spending the spell's slot.
5-7: The spell fails without spending the slot; may try again next round.
8-18: The spell succeeds, spending the spell's slot.
19-20: The spell succeeds without spending its slot.
21+: The spell succeeds, spending its slot, but with double effect.
Being that most sacred spells are supportive, I would also allow a casting in the space of ten minutes without having to roll on this table. This does the least damage to the balance of the cleric/priest class, while still making them feel that they are making a "desperate petition" in the heat of battle.
Next up: A completely different approach based on reaction and morale rolls.