I don't think I would say "ride a swing" or "swing a swing." I would say "Do you want to go swinging?" or "Do you want to swing?" or maybe "Do you want to play on the swing?" I'm from the U.S. . . not sure if it's different in the UK.

Out of curiosity I looked if wikipedia would hint a proper verb, but they sneaked out of this question by saying: "A person using the swing..." That's probably too formal, but wouldn't be wrong either.

I have asked my kids if they want to swing on the swings. But more often I ask them if they want to go for a ride on the swings. I think you'd be ok with either. I'm from California.

Hi Maria, Brendon here. You could definitely say, "ride on a swing". In this context, the word "swing" is a noun - that's the name of the object you're riding on. In the US, you ride on the swings (swings being the name, ride being the verb). Grammatically, it's correct to inquire if one can "swing on swings", because "swing" is an action verb and "swings" is the name of the object in which you're swinging on, which is inherently a noun. Surefire method is to say, "can I ride on the swings".

'Swing' is a verb, but if you're talking about the play equipment. I'd say 'go on a swing'. 'Daddy, can I go on the swing?' 'What did you do at the park?' 'We went on the swings.' This may be different in other English-speaking regions.