How does the courtship method of a swan differ from that of a peacock?

Swans are monogamous and form long-term or life-long pair-bonds.

Peafowl are polygamous and have no pair bond at all.

Cobs and pens will pair to begin with using imperceptible gestures and rituals. Between the pair that forms, courtship consists of exaggerated preening and feeding movements

Peacocks are competitive amongst themselves and will only be chosen by a hen for mating when they have a full train (often called tail or fan) and can perform the correct ritual movements. Displays are flamboyant and designed to mesmerise the peahen.

In simpler terms, a swan uses sound - a song

a peacock would use a magestic display of feathers to attract mates.