The cover has split, so I need to buy a new one or replacement cover (it is attached with dowels), but I do not know who stocks them,  any advice will be most appreciated.

Stores like Homepro or Global House usually have this "outside furniture", i never payed attention if they have deckchairs, but probably they have

I forgot to include that I am in Jomtien.

Save your time, there is a small shop on Theprasit road that has what you need.  Left side, going towards Sukumvit about 1km from Thepraya road.