OK, the question is "How Should the Paladin Suffer".
I opened the thread, read the first post and my response is: That isn't the DM's decision. That is the player's decision.
If the player is role-playing, the paladin will suffer plenty when he finds out. The DM does not dictate how the character is played. That is what NPC's are for. However, if the player does not RP any self-induced suffering, then there may be need to encourage it. Or, you might be expecting more pathos from a player that really doesn't want to give it to the game.
As for what kind of penalties the paladin might suffer, I am a little troubled on this. It isn't clear that the paladin did anything wrong, really. There are a few things that people have touched on here in the thread.
First of all, a paladin does not need to have a deity. A paladin can have a deity, but the paladin can derive powers from nothing more than a noble and pure purpose. This is where I usually go off on my assertion that the Code of Conduct can be different for each paladin. Indeed, a unique Code of Conduct is what I tend to expect in my games. This is not to say that the Code of Conduct won't share many similarities between paladins, but their emphasis need not be identical. In this case, the paladin might put a strong emphasis on Hope, Love and Family, while another paladin might put the emphasis on Righteousness and Justice. Both paladins might believe in all five of those things, but the emphasis will be different and in some situations the two paladins could disagree on the best course, because of their individual emphasis on what is best.
Second of all, Detect Evil is a spell-like ability, but that does not make it very subtle. In fact, spell-like abilities can draw attacks of opportunity. They can ine interrupted and require a fair amount of concentration. They may also have a visible or audible affect associated with them. In many polite societies, it would be reasonable to expect a Detect Evil to be considered rude. As well, being evil does not give a paladin carte blanche to smite on sight. Unless of course, you want to run that sort of campaign.
Third of all, there is a big difference between a Vow and a promise. You need to very carefully think through your enforcement as a DM. If a paladin Vows to serve and protect a King, what will happen if the King sends the paladin off on a quest? Or to lead an army? Or to act as an Ambassador? If an assassin kills the king while the paladin is away, will you penalize the paladin? After all, he should have stayed by the King's side, he did Vow to protect the King, right? Of course, he also Vowed to server the King. Is this an interesting quandry? Or, were you setting the paladin up for failure? Is there any "punishment" that needs to be administered? Or, should you let the PC agonize over it themselves? This can be an opportunity for RP, but where should the DM step in an apply external pressure by denying paladin powers.
You want to think all of this through carefully. You will be establishing a tone for the game, and how you expect characters to behave. Depending on your players, and why they enjoy playing the game, you might find their reaction to be unexpected.
In this particular scenario, you need to understand what tone you want to set.
Is a promise to a little girl a solemn vow? Certainly, it might be to the little girl. It may, or may not, be to the paladin. What about to reasonable observation? What about to the gods, or to the universal concept of Good that the paladin derives power from?
If you hold this up as an example of a solemn vow, are you actually telling your players that they shouldn't make any promises to NPC's because the players don't know how it will be twisted back on them? Will you establish an adversarial stance with your players?
Or, does this vow only have power because of the belief of the little girl? If that is the case, is it enough that she somehow haunts the paladin, and perhaps the whole party? Is it necessary to move toward stripping powers from the paladin? Do you trust your players to RP all of this in an interesting way that tells a grand story without resorting to a mechanical penalty? Or, are your players the sort that might not appreciate any sort of emotional struggle and can only relate to mechanical penalties?
There is a lot of potential to turn this into a wonderfully moving story that has repurcussions throughout the campaign. A lot of that will depend on how your players deal with it, because there is also a lot of potential for the players to be resentful of the "paladin trap".
If it were my campaign, I would probably have the trust and perceived betrayal of the little girl be the motive force for dreams. I would give the PC's enough information to suspect that something bad ended up happening. I would let the PC's figure out the mystery and then tell me what kind of "suffering and punishment" they feel. I would let them tell me how to resolve the situation to their satisfaction. Some of my players would feel very little pathos for the situation. Some of my players would treat it as a wonderful opportunity to agonize over past mistakes and investigate new characterizations. Both types of players enjoy my game for different reasons. I'm OK with that, though I would love to see all of my players go for deep, immersive characterization.
Find the balance for your group where you can have pathos and fun.