Mmm, feel like getting up early in the morning for the next couple of days?
If he comes around during the day you are probably ok with it only being set then. You probably have some other nocturnal visits at night. You've said before there are coons around, right? If you could leave it out until around 10 PM and then bring it in you might get him then. He may feel more comfortable.
Covering the trap may make the kitty feel a bit more secure. If it does not look like a trap he may be more likely to go in. I used an old blanket a few times when I left it out.
This is only the second day you have had the trap. I have a feeling you will catch him.
Hate to ask but is there any possibility that this cat is female and is nursing a litter? I know you have seen him/her so will know.