I don't think any skill rolls can directly dial you in to your character's deity. As a DM, I wouldn't allow it, though I wouldn't be above letting Divine characters getting a good/bad feeling about things in situations where they might be closer to their deity, like while praying in an appropriate temple, or at a certain altar, etc. As a player in a recent campaign, my cleric of Ioun was getting visions in dreams from the get-go, indicating he and the party-to-be was pivotal in some prophecy, so he figured he was special enough to check in on the party's progress now and again, whenever he was at an altar or shrine. Occasionally the GM would humor me and say something like, "You get a feeling like a pat on the shoulder, as if to say, 'Good cleric.'"
What I think is more important to recognize in these situations is not that your players are looking for direct divine information for its own sake, but that they may feel that a sense of continuity, or of the plot affirming their actions, is lacking in general from the game. This is really an out-of-game issue; if there's no real sense of why the characters are doing what they're doing, then the players will question what's going on. As GM, it's your job to either provide that directly, or to keep checking in with the players as to their characters' goals, and how those will affect the direction of the campaign. Either way, it could be that your players' expectations and your own aren't in sync.
Or maybe I'm reading too much into this. :) If your campaign isn't serious and was based on the premise of "we need something to do Wednesday nights so I'm gonna throw some monsters at you, roll up," then it doesn't matter and you could just remind your players of this.
Edit: I just remembered the Hand of Fate ritual (link to DDI), level 4, divination.
When you perform the ritual, ask up to three questions about possible courses of action. A translucent blue hand appears and indicates with a gesture what the most rewarding course of action is.
...and then it goes on about the specifics about how the Hand will go about answering questions, and why it's not an easy cop-out, circumvent-the-DM ritual. So, not a direct line to a deity, not cheap (it's 70gp in components), but it's there.