big (esp. BrE)
He gave her a big cuddle and told her not to worry.

have (esp. BrE)
They were having a cuddle on the sofa.

give
Give Daddy a big cuddle.

a kiss and a cuddle (BrE)
He just wants a comforting kiss and a cuddle and he'll be all right.

Cuddle is used with these nouns as the object:
baby