If I was a spellcaster, I would cast a couple 1hr/lvl spells on myself throughout the day and try to gauge when 15-16 hours have passed so I know "when-ish" to go to bed.
Other than that, I'd make it a Survival check with a significant DC to know exact time, if they fail the check by 5 or less, they might know what time it is +/- an hour or two, if the check fails by 5 or more, they probably wouldn't have a clue.
Honestly, I don't think it is that exact. If you pray at 'sunrise' I don't think it is at precisely the second that the sun becomes visible or anything like that, just around that time. If you can't, presumably in this case because you weren't aware that it was the right time, you just need to do it when you get a chance, presumably when you do realize the time has come. So cleric wakes up, thinks it is maybe morning, tries to pray, gets nothing because it is too early, waits a bit and tries again and it works. Or wakes up late because it they didn't realize what time it was (prevented from praying at the right time) and then they go to pray and it is all good.
Personally, I doubt that trying to be heavy handed on enforcing an exact time will add fun to your game, so I'd generally let them get their spells as normal.
For a divine caster, I'd probably just have them "know". For an arcane one, whenever they get tired and rest eight hours, that's good enough for me.
"Per day" abilities other than spells are pretty nebulously specified. I've never been certain whether they're supposed to come back 24 hours after use, after 8 hours rest, or at a specific time of day. Fortunately, it only comes up a couple of times per campaign, and I usually just handwave it when it does unless someone's actively trying to exploit things.
If you decide that knowing when to pray isn't possible without being able to see the sun because you feel it is more realistic and fits the mood you want then I think you will also have to explain how the locals divine magic gets around that problem.
Also, while there are certainly real world tribes that don't look at time the way we do, particularly in dividing it into discrete elements, I am pretty sure that there are not any real world tribes that don't have any concept of time. Day and night, youth and age, past, present and future are all pretty fundamental concepts for anyone.
I get presenting your players with a challenge and encouraging them to come up with creative solutions, but I still don't think this particular point will add fun to your game. One big question is how will the PCs discover this is a problem they need to solve. I've participated in multiple 'dungeon delves' that lasted more than one game day and never had a GM say we couldn't get divine magic because we didn't know when the sun came up, so I wouldn't expect them to anticipate this problem ahead of time. If their first clue is 'your prayers don't work, say goodbye to your main class feature until you figure out when sunrise is' I don't think they will find it a 'fun challenge.'
I would suggest that if you need something mechanical to throw off the players due to weird environment you make it a bit less significant to any single character and applicable to all characters. Something like if they can't get themselves a clock they each have to make a fort save or still be fatigued after a sleep period.
I just want to clarify that divine spell casters don't need to pray and prepare spells at sunrise.
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.Time of Day: A divine spellcaster chooses and prepares spells ahead of time, but unlike a wizard, does not require a period of rest to prepare spells. Instead, the character chooses a particular time of day to pray and receive spells. The time is usually associated with some daily event. If some event prevents a character from praying at the proper time, she must do so as soon as possible. If the character does not stop to pray for spells at the first opportunity, she must wait until the next day to prepare spells.
Now, this could produce situations where a caster could be denied their magic. But honestly, as a player I would just be upset if you denied me my main class ability. Just don't.
If nothing else explain it as "Your deity understands your circumstances, as long as you continue your daily rituals to the best of your abilities you continue to receive your spells".
You could use an hourglass. Have a wizard's familiar watch it and when the sand runs out it makes a mark. Then it turns it over again and keeps watching. It would let you know how much time has passed. If you don't have a familiar, you could use 2 unseen servants with the hourglass. One to turn it over when the sand runs out and another to make a mark every time the hourglass turns over.
alternatively you can spend the 1k gp on a water clock. Provided they have access to a source of water to keep it running.
Unless your players are for it, don't take away their toys. The code that Claxon points out that deities are understanding. They are not "oops, you missed your normal 4:01 ritual, and it is now 4:02. Better luck tomorrow".
If your players make an effort to keep spells and track time in any way, let him prepare his spells.
I just want to clarify that divine spell casters don't need to pray and prepare spells at sunrise.
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.Time of Day: A divine spellcaster chooses and prepares spells ahead of time, but unlike a wizard, does not require a period of rest to prepare spells. Instead, the character chooses a particular time of day to pray and receive spells. The time is usually associated with some daily event. If some event prevents a character from praying at the proper time, she must do so as soon as possible. If the character does not stop to pray for spells at the first opportunity, she must wait until the next day to prepare spells.Now, this could produce situations where a caster could be denied their magic. But honestly, as a player I would just be upset if you denied me my main class ability. Just don't.
If nothing else explain it as "Your deity understands your circumstances, as long as you continue your daily rituals to the best of your abilities you continue to receive your spells".
Meh, it's not as bad as it looks so long as you aren't getting an entire day's worth of encounters after missing the deadline. If you're storming the castle and it gets hairy and the last encounter just makes it past the deadline for recovery, it's no worse than if things had gone faster but still had the same number of encounters.
A guideline: If a string of encounters is planned to stretch over the course of two or more days without a chance to rest, make sure the balance the whole interval as though it were a single day. This may give an edge to classes with per-day abilities, but casters won't really be penalized unless they've fallen into a "it's 9 pm, time to burn all my spells" habit--which is a habit that needs breaking. : D
Oracles don't prepare spells, they only get back spell slot once every day (regardless of when/if they sleep), and 'after I get up' is not a time of day.
This may give an edge to classes with per-day abilities, but casters won't really be penalized unless they've fallen into a "it's 9 pm, time to burn all my spells" habit--which is a habit that needs breaking."It's 9pm and we're in a relatively safe place with the door barricaded. It's safe for me, the healer, to top off the party's HP."
I play an oracle, and my GM knows that, if we "rest", I'm burning spells to top off the party of those trifling 2 or 3 HP I wouldn't waste a Cure Light on normally.
Sure, in that case. : ) But burning your last fireballs on some dire rats for the lulz might come back and bite you if for some reason a challenger appears before you have a chance to rest.