I would ditch the newspaper and liners, both will hold smells and liners often end up leaking anyway if you have enthusiastic scratchers
. I'd go for a clumping litter like Cats Best that Dawn suggested where you only have to remove the clumps of wee (and solids of course!) and the remainder of the litter stays clean and dry. You use less litter and don't need to dump every day.
I used to have all my trays in a large walk in cupboard, didn't have a problem with lingering smells. The only reason I moved the trays out of the cupboard, was because I have 8 cats and I started to think it wasnt ideal for them having to go all in the same place (bit like a busy public loo!) so I relocated them to different areas, bathroom, spare room, bathroom and hallway.
I wouldnt use air fresheners in the cupboard either, cats sense of smell is much more sensitive than ours and can put them off - the Neutradol that Jez mentioned is a better alternative.