There's a technical aspect to this question, in terms of whether the buyer has the right to keep it, and I think that sheds light on the broader question. In Jewish law, the combination of the original owner's despairing of recovering his or her stolen items and a change of possession, makes the item no longer the original owner's. That is, if Jack's car is stolen, in such a way that Jack loses hope of ever getting it back, and then is sold or given to a third party, even if Jack then sees the car, by Jewish law it is no longer his (restitution has to be made, of course, and who pays what is a whole different discussion). That doesn't mean it's ok that this happened, it means that when it comes to possession of items, Jack's claim on the car ended when it was taken from him, he despaired of recovery, and then it changed possession.
I bring this up because it shows that in the case here, there would be a good likelihood that the item itself could belong to the buyer even if his suspicions were true. It might be that he'd have to make some kind of financial restitution to the original owner (although that is really supposed to be the thief's obligation), but the item itself has been removed from the owner's hands (and not by the buyer). Such technical details are usually not relevant to parsing moral questions-- I wouldn't, for example, recommend buying from a "fence" because of this rule-- but the complication that the buyer only has suspicions makes this aspect of it another mitigating factor to consider.
What's also not clear in the question is what fueled the buyer's suspicions-- a queasy feeling, the fact that the seller had greasy hair, or because of an overheard phone call where the seller said "yep, just got rid of the hot goods now."? If there's truly no evidence, such that the buyer has no grounds to even alert the authorities, I wonder whether these suspicions have much justification.
Assuming they do, assuming that something happened that makes it fairly clear these items were stolen, we still don't know who stole them, nor do we have any ability to figure out from whom they were stolen. If we did, we could recommend tracking down the original owner and returning it, as a good deed. Since that seems to be impossible, it would seem the buyer has, through no fault of his or her own, come into legal possession of items with an unsavory provenance. The question is how to salve a conscience that knows it has some connection to, but no guilt for, a wrong that was done.
One possibility is that the item is the problem, and then selling it might be more comfortable even if it doesn't alleviate the moral problem. A better solution might be to donate the item to someone in need-- this does nothing for the original owner, but we can't do that anyway. This way, the buyer doesn't have to see the stolen item all the time and can feel that at least some good came out of it. If the item doesn't bother the buyer except insofar as it leaves a nagging feeling, the buyer could donate the value of the item to a charity; not that I believe we can "buy off" our wrongs, but in this case, the buyer hasn't done a wrong, he or she has only come to feel connected to someone else's wrong. This would be a way to ease that conscience. And maybe having the item around will be a spur to avoid questionable activity of all sorts going forward.
Answered by: Rabbi Gidon Rothstein