City (78 points):
Home: Brighton, Scum, Swansea, Huddersfield
Away: Stoke, Everton, Spurs, West Ham, Southampton
27 points available. The schedule really breaks kindly for City except Spurs away. If they beat Stoke and Everton they'll already be on 84 points before the derby. Either Liverpool or the scum will drop points before that match so best case for them will be either 69 (Liverpool) or 72 (scum). So after the derby (assuming City win) City will be on 87 points with 6 games left to play so they should still be up 15 with 6 games left to play.
Liverpool (60 points):
Home: Watford, Bournemouth, Stoke, Brighton
Away: Scum, Palace, Everton, West Brom, Chelsea
27 possible points available. They'll be favored in all of their matches except maybe their match at Stamford Bridge. Everton may play inspired football and get a draw though. I'd give them 83 points.
Scum (59 points):
Home: Liverpool, Swansea, West Brom, Arsenal, Watford
Away: Palace, West Ham, City, Bournemouth, Brighton
30 points possible. They'll be underdogs against Liverpool and City but the rest of their schedule shouldn't be too much of a problem for them. I can see them finishing strong and getting 24 points which puts them at 83.