Once an ability that causes a creature to connive begins to resolve, no player may take any other actions until it's done. Notably, opponents can't try to remove the conniving creature after you discard a nonland card but before it receives a counter.
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If no card is discarded, most likely because that player's hand is empty and an effect says they can't draw cards, the conniving creature does not receive a +1/+1 counter.
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If a resolving spell or ability instructs a specific creature to connive but that creature has left the battlefield, the creature still connives. If you discard a nonland card this way, you won't put a +1/+1 counter on anything. Abilities that trigger "when [that creature] connives" will trigger.
When Toluz enters, it connives. (Draw a card, then discard a card. If you discarded a nonland card, put a +1/+1 counter on this creature.)
Whenever you discard one or more cards, exile them from your graveyard.
When Toluz dies, put the cards exiled with it into their owner's hand.
