Obviously, the other team would have to value marner high enough to give up a 1st. pairing defender.
Depend on the different positions posters take with regards to marner, some teams would give up any player on their team if they believe he's equivalent to Matthews. So if that is one's position, (I believe you are in this camp) you could name probably at least 15 #1 defenders in the league, and that defender would be making much less than the amount Matthews is making (the amount some suggest marner is holding out for).
I'd probably take one of those, in addition to that player I'd have cap room left to address defenders going forward. If they over pay on marner someone has to go in the next couple of years on defense and they will have to back fill with prospects or depth defenders.
If his value isn't that high, you shouldn't give in to his demand but if he won't budge you move him for valuable assets, which could include a combination of players, picks, prospects. Without much thought a defender, prospect and pick from Carolina might work ('Canes have an extra 1st.). You could go around the league looking for a similar return.
I'd rather marner signs to a workable contract in Toronto, but if it just doesn't work (and there is a point where it won't) you move on and put the franchise 1st., as all team fans should demand.
EDIT: Seems like a good poll question, Would you trade Marner if it made the team better? Y/N