There are some things that Divine Magic doesn't do -- at least, outside of domains. One of the first that comes to mind is Instantaneous travel -- Teleport and Dimension Door spells. Without taking the travel domain, those spells are out of reach to a cleric. And, at higher level, those spells are as important to party success as healing spells are, one could argue.
You might look to arcane magic to do something like speed up time -- so that over the course of ten minutes, or an hour, the spell would speed up time in a localized way that allowed the subject to heal as if she had just had a night's rest. That would be a healing spell that did not rely on divine magic or energies, but simply the natural healing ability of the subject. This would be a sort of low-end regeneration -- it wouldn't restore lost limbs, etc., but it would allow for some faster recovery time. The closest thing to a precedent for this spell would be the natural healing that Polymorph provides -- perhaps the spell would be related to that, a sort of transmutation.
Also, the spell's casting time would be a minute, not a standard action, so it would not be a good combat spell, but only really suitable for non-combat situations.
As far as staging the spells would go, you could create a first level version that allowed one day's rest to pass in a minute's time. The second level version would allow for two days. And so on up to 4th leve. 5th level, just like the Cure Wounds sequence, would be a mass version of the first level spell.
Another option: Allow the caster to maintain the concentration for an additional minute for every caster level, but require a successful concentration check, DC 10+ 5 per minute level for each additional minute (added on cumulatively). So a 3rd level wizard could cast the first level version this, foster natural healing for his barbarian friend over the course of three minutes, needing to make no concentration check for the first minute, a DC 15 check for the second, and a DC 20 for the third. If he succeeds and is not interrupted, the Barbarian will recover from his wounds as if he had complete rest for 3 days.
Because of the way hit points work in the game -- and the way PCs recover hit points over time -- it will take roughly 8-10 days of rest to restore a fighter to full strength from 0 hit points. To do so with the Rest And Recovery spell, it would mean casting the 4th level version AND maintaining it for a second minute, or maintaining the first level version for 10 minutes (which would build up to a stupidly high DC on the concentration check)
Oh, and throw in a +2 synergy bonus on the concentration check for 5 ranks in heal.
-rg