Sailrite used to sell SS grommets in smaller sizes, they probably still do. You need some special equipment to install larger SS grommets.
Brass will do nicely in a trampoline, I had a homebuildt one for several years on an old Tornado (saltwater sailed, north sea). For sails, brass grommets are not strong enough for halyards, downhauls etc.
If you decide to go for brass grommets, and install them with the tool and a hammer, take care to fill them with cloth and dont overdo it when you use the hammer. You will get a sharp edge on the inside, where the lacing runs, if you do.