My kitty doesn't have a particular time of day he prefers. Any time I sit in front of the computer, he appears from wherever he was hiding and jumps up on my lap. Then I have to swivel to the side and put my feet up on the couch next to the computer desk, so he can lay on my legs. He will only lay on my upper legs, not my torso. This makes it very difficult to type, being turned to the side with a big purring kitty on me, about to fall off of my legs. I've learned to type one-handed quite well.
On rare occasions he will jump up onto me when I'm on the couch watching TV. If I am seated, he will wait patiently until I get a clue and lie down, because he won't lay on my legs unless they're stretched out. (He actually lays more in the juncture of my legs and torso - he's very weird.)
Even if he's not actually cuddling with me, he likes to be in the same room as me, especially the computer room. He will curl up on the couch, often on top of important papers, and sleep there for hours. All of the cuddling he does, though, is definitely on his terms, instigated by him, and ended when he's had enough.
The legend says that Mohammed adored cats. When one of them was sleeping on his sleeve and he had to go out, Mohammed supposedly cut off the sleeve so as not to disturb his pet.
A righteous man regardeth the life of his beast - Proverbs 12:10
How we behave toward cats here below determines our status in heaven. - Robert A. Heinlein
What greater gift than the love of a cat? ~ Charles Dickens
There is, incidently, no way of talking about cats that enables one to come off as a sane person. - Dan Greenberg
If purring could be encapsulated, it'd be the most powerful anti-depressant on the market. ~Alexis F. Hope