In general, they can use any magic items that are available to all PCs. However, I think you're looking for items that are most useful to this specific class. Because the class is not fully supported with official rules, I would create items that support the class.
Are they focused on alchemy or guns?
If guns, I think you can come up with a variety of magic items that mimic real world gun technology. You might reskin a wand of fireballs to be a grenade launcher that attaches to their weapon. You might add a scope that allows the character to use a bonus action to double their ranges until the end of their turn. You might decide it would be fun to give them an area attack that is essentially a machine gun. Or make armor piercing ammunition (that reduces enemy AC - useful when combined with advantage). For book items, anything that allows them to gain altitude or see better would make obvious sense, as do the Figurines of Wondrous Power.
If alchemy, I would look for things that increase range. I gave a magic cesta to the alchemical artificer in my game. It allowed him to throw his 'potion balls' much farther, as well as catch certain things. I also provided him with a kit that allowed him to test magical residue to discover what spells had been cast in a particular place.