From what you describe, the department gives you free rein to decide whether to supervise a student (which seems fairly normal, based on this Academia SE post, and my own experience in US universities), so the only issue is how to convey your choice in a polite and professional way. For that I suggest giving impersonal reasons and offering alternatives.
If you feel the need to give reasons (or they press you), do try to make them as impersonal as possible. For example, I had a request rejected in college because "I've only had you for one class": it couldn't be changed or argued with, and had nothing to do with personal judgement. Another point may be different research interests, if the student wants to do a project about something that is not your particular area of interest. This came up often for my college's senior projects and some final projects in grad school; students were expected to find a faculty member with similar research interests for their projects, so we typically had an informal interview or at least emailed a proposal to see if the project idea was reasonable and compatible.
Of course, don't invent reasons that wouldn't otherwise apply! I think you know this already, based on your comment about claiming "too busy", but I want to be very clear that this is about examining your existing principles for accepting students and picking out the least personal ones to say.
I will add that I strongly disagree with the answers here implying that you should feel obligated to supervise students that have been difficult and unpleasant in your classes because you don't have an qualitative metric by which to rule them out. If your declining is problematic for the student in some way, it's the department's responsibility to sort that out. But since you have the choice, both you and the student will be better off if they find a supervisor who actually wants to work with them. This leads to my last suggestion:
"Sorry, I don't think it would be a good fit."
(or a variation thereof - "I don't think I would be a good fit" could work well too, as suggested in a comment.)
It's a bit of a cliche, but it is an honest reason without giving much of anything away. Similar to baldPrussian's answer, it has minimal "attack surface" because you aren't being too specific - and like that answer, I also recommend resisting the urge to elaborate since it will only provide them with things to argue about.
The next and probably more important part is immediately following it with an alternative - that might be suggesting a different lecturer to ask, or guiding them to a list of projects open to students, or whatever resource you might have. Going back to the professor I mentioned earlier, I had asked for a recommendation letter - her full response was basically: "I've only had you for one class. Why don't you ask one of your professors from [other class]?" While the rejection still stung, as rejections often do, I was grateful that she suggested a path forward and redirected my energy towards that new path; no reason to argue that she specifically had to be the one to write it since I now had another option. Hopefully your students can be similarly redirected!