Implemented via an additional option at the relic selection screen that lets you pick 'Cursed Relics,' which are the same as regular relics but allow you toggle one or more curses. A word other than Cursed could be good so there's no overlap.
Alternate- winning teaches you a secret code/character name to enable curses when typed on the screen. I suggest 'FERRETOP'
Inert- Your relic gives no starting skills or upgrades. You will not earn any upgrades either, and cannot learn skills.
Only Human- You do not earn experience.
These two might be dull exercises in letting your demons do everything and not getting hit, but I'd hope they'd be good for a giggle. Or at least a death rattle.
Entombed- No items or currency spawn. SEPI and Recycle might still work...
Complete reliance on 'Starting Packages' and wild modified demons. I might try it myself as a conduct. Might need a 'No Uniques' clause...
Infamous- 90% of demons and all Uniques spawn with Distrust.
Having incredibly limited demon recruitment access would force some very creative builds I think, the whole 'necessity is the mother of invention' thing. This one is the main reason I made this post.
Solo- Only 1 summoned demon at a time. Alternately, Relic Capacity=1
I've haven't retried this conduct for a while, but I always thought it was pretty interesting so long as you resisted the urge to kite things to death with Vigor Siphon and pillar dancing.
Eternal Punishment-All enemies are Heroic. Even enemy summoners and ghosts. ESPECIALLY them.
It's the only way to stop Ayayaya!