Cats are very clean animals, a lot more so than dogs anyway (if it looks fun, they want to roll in in types haha).
He's never once not used the litter tray and it has to be regularly emptied as a cat won't even use a dirty or smelly litter tray :)
Have you noticed a pattern between when pup eats and when he needs to go? You could adjust meal and sleep times to try and encourage him to go beforehand?
It would usually be about half an hour after sleeping, playing, feeding or drinking as he's only little and won't have developed a very strong system as yet. Routine could help him and associating words with his business (wee wee, poo etc...).
Voice tone can be useful as well, a gentle but firm no when he's done what he shouldn't and praise when he's done something good. These should be done right after him doing what he should do so the association is there for him.
This might help...
http://www.thekennelclub.org.uk/item/458