We have tried all the tricks that have been suggested to train a kitten to
pee in litter box and he is still peeing on carpet.  Here is the background
and what we have done:

He is 3 months old. (had him since he was 8 wks......a loving purring
kitten...great personallity except litter box issue).  He has a litter mate
sister who used the box always.
When they are closed in the kitchen area, he will use the litter box always.
When we let him out to explore the house.......(limited to living room for
now)
He will sometimes pee in a certain spot on the carpet.
We will pick him up every time as soon as we see and put him in the litter
box.
We clean w/ enzymatic cleaner to remove smell each time.
He still pees on the spot on the carpet.
We then covered area so he does not have access and he finds a new spot to
pee in another part of the room on the carpet.
Again we cleaned and deorderized and put a 2nd litter box on the spot on the
carpet in the living room.
He will approach the 2nd litter box box and pee just outside of the litter
box on the carpet.
We cleaned again.   This repeats for a few times.
We then started to spritz him with a water spray when he start to pee.
He will run and then immediately pee on a new spot against the wall on the
carpet.
We have seen him use the 2nd litter box to poop in.
He has a litter mate sister who uses the primary litter box always in the
kitchen.
Again, never accidents in the kitchen.

Any new suggestions?  At this point we hate to let him out of the kitchen
area until see some inclination to pee in the litter box.

Thank you for the advise:)