Can I convert a 240V dryer to 120V?
Switching out the cord is easy, but that does not make it a 110V dryer. It's probably not possible to convert to 110V, although you'd have to find a user manual or contact the manufacturer to confirm. And even if you could, it would probably draw more power than a standard residential 110V outlet could supply.

The only way to do this is to run a 220V outlet for the dryer. Do you rent or own this apartment? What country are you in? Most US service is 220V, even if all of the outlets are 110V.