Oracles and Inquisitors can be extrapolated from how sorcerers and bards prepare their spells, as Oracles and Inquisitors aren't mentioned in the core rules for preparation time:
Each day, sorcerers and bards must focus their minds on the task of
casting their spells. A sorcerer or bard needs 8 hours of rest (just
like a wizard), after which she spends 15 minutes concentrating. (A
bard must sing, recite, or play an instrument of some kind while
concentrating.) During this period, the sorcerer or bard readies her
mind to cast her daily allotment of spells. Without such a period to
refresh herself, the character does not regain the spell slots she
used up the day before.
Unlike a cleric, an oracle need not prepare her spells in advance. She
can cast any spell she knows at any time, assuming she has not yet
used up her spells per day for that spell level. Oracles do not need
to provide a divine focus to cast spells that list divine focus (DF)
as part of the components.
An inquisitor casts divine spells drawn from the inquisitor spell
list. She can cast any spell she knows at any time without preparing
it ahead of time, assuming she has not yet used up her allotment of
spells per day for the spell’s level.
Oracles and Inquisitors are subclasses of Cleric, as Bards and Sorcerers are subclasses of Wizard (sort of!)
Clerics meditate or pray for their spells. Each cleric must choose a
time when she must spend 1 hour each day in quiet contemplation or
supplication to regain her daily allotment of spells. A cleric may
prepare and cast any spell on the cleric spell list, provided that she
can cast spells of that level, but she must choose which spells to
prepare during her daily meditation.
Note also that Sorcerers also have the same sort of preparation quote text:
Unlike a wizard or a cleric, a sorcerer need not prepare her spells in
advance. She can cast any spell she knows at any time, assuming she
has not yet used up her spells per day for that spell level.
I would, therefore, suggest that these classes refresh in a similar way to their quasi-parent class:
Sorcerers need 8 hours of sleep and 15 mins concentration then they have their new spells.
Oracles and Inquisitors need to wait until the special "refresh time" and then spend 15 mins in prayer and then they have their new spells.