The only time I’ve ever needed to add a capacitor across a relay contacts was with a 12v AC door release mechanism (the type used on door entry systems, where the door lock makes a buzzing noise when the lock has been released).
I experimented a little and eventually settled on a 220uf non-polarised capacitor.
In your case the capacitor will need to be rated at your mains voltage or higher. Be careful when doing this, as capacitors can store a large amount of power and give you a nasty shock unless you discharge them.
Pete.