Let me chime in here. A few things come to mind.
First, a priest needs actual sin to absolve. It really makes no difference what someone “feels” is a sin, to them. That philosophy has a name, and it’s called relativism. Normally, we think of relativism in these terms, “Well, maybe for you having sex outside of marriage is a sin, but it’s not for me.” We rightly criticize this viewpoint. However, what is being espoused here, as far as I can tell, is no less relativistic. Let’s use a real example rather than hypotheticals. Someone who is pious may feel very badly about missing Sunday Mass for any reason, even if there’s a blizzard, the person is 85, and is suffering from a cold. He/she may FEEL that missing Sunday Mass was a sin, but that doesn’t change the fact that in this case, it WASN’T a sin. This may sound harsh, but whether or not something is a sin is not defined by how it makes us feel. Indeed, many sinful things make us feel quite good (that’s why we go back to them), and many virtuous things can be quite painful.
Second, I would caution anyone against mentioning past sins. Again, the priest can’t absolve what has already been absolved. Just like you can’t rebaptize someone who is already baptized, you can’t reconfirm someone who is already confirmed, and you can’t reconsecrate hosts that are already consecrated, you can’t absolve sin that has already been absolved. If God has forgiven said sin and let it go, we should too. In fact, I can’t think of any scenario where it would be advisable to dwell on past sins. This sounds dangerously close to despair.
Third and finally, if someone TRULY can’t think of any sin, then there are two options. First, forego the sacrament of penance. It’s surprising for people to learn, but the Blessed Virgin couldn’t go to Confession. Leaving aside the historical development of the sacrament for a moment, it was literally impossible for her to celebrate the sacrament because she literally had no sin to confess. The second option is to find a better examination of conscience. I don’t mean for that to sound harsh. I mean it quite literally. Sadly, some of the examinations out there today are abysmal. They either only focus on the really big stuff, or they are so banal that they can’t possibly help anyone examine his or her conscience. “Have I failed to love others?” “Have I failed to see Christ in other people?” If you’re breathing (and you’re neither the Word Incarnate or the Blessed Virgin, then if we’re honest, the answer is YES!")
If you have a smart phone, there is a good app available called “I Confess.” It has an excellent examination of conscience based on the 10 Commandments, the Precepts of the Church, and a few other things. I recommend it wholeheartedly.