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This is my take on competitive CSM and Daemons and also staying away from daemon princes.

It's a pretty straight forward list.. with plaguebearers walking up the field taking control of the board while my Pinks and Letters in deep strike to tie up key units.
The Jump pack chain lord with relic, sorcerer and dark apostle walk up with plaguebearers to take out big threats.
And the contemptors sit in the back with the other lord taking out armour units. 10 reinforcement points for blue horrors..

The List

++Chaos Daemons Battalion++
+HQ+
Changecaster - Staff of Change
Poxbringer
Sloppity Bilepiper
+Troops+
30 Letters - Icon, Instrument
30 Pinks - Icon
3 Nurglings
x2 30 Plaguebearers - Icon, Instrument

++Supreme Command++ Black Legion
+HQ+
Chaos Lord w/ Jump Pack - (Warlord - Flames of Spite) x2 Chain Sword(Relic - Ghorisvex's Teeth)
Sorcerer w/ Jump Pack - Force Axe, Diabolic Strength, Prescience
Dark Apostle - Soultearer Portent, x2 Dark Disciples

++Vanguard++ Alpha Legion
+HQ+
Chaos Lord
+Elites+
x3 Hellforged Contemptor Dreadnough - x6 Butcher Cannons

But the skullreaver daemon prince is sooooo good!!

But seriously these lists work well by hiding behind screens of horrors, plaguebearers and bloodletters. It's a shame to give long range anti tank a target. As good as the contemptors are they'll get popped quickly if they're the only target and are not in combat as quickly as possible.

If you want to stay clear of daemon princes I would go for exhalted flamers, maybe some blighlord Terminators, oblits, csm termies or scarab Occult, over the contemptors. The master of executions and greater possessed are great beatsticks you can hide too.