My pup is still going on our rug if we don’t move fast enough. He doesn’t like being outside in the rain, and he is still so very young, and small, and shivery, and squeaks and whimpers at the back door so soppy here lets him in - for the sake of the neighbours, you see, and not at all because I’m cold and damp as well.
As FeedThemFlumps says, you need to get them outside LOTS:
As soon as they wake up
As they walk away from food/water bowl
As soon as a play/greeting session calms down
If they turn in a circle (Elfpup misses this stage, but all our other dogs circled prepee)
If their knees sag - move FAST!
The rug needs cleaning, ideally with something to eradicate the pee smell. It would be ideal if you could remove it for a week or so (hang it up to air in your garage/in your garden, if it ever stops raining) until the habit is broken and the pee smell (a cue to pee) is totally gone.
And just keep on with fulsome praise for peeing where you want, and ‘the disappointed voice’ at any accidents. (My Oscar is in the post 
)