How can I darken the color of painted furniture using varnish?

Varnish has a yellow cast to it and yellows over time. It would not darken the color. it's just a protective finish.

Maybe dry brush a darker gray over it?

I would recommend using antiquing wax. That will darken and add dimension to your finish

You could use a dark antique wax or paint it a darker color before varnishing

If its a painted set then a dry brush of a slightly darker color would definitely work. If its stained you could consider going over it with a gel stain - make sure and wipe it down thoroughly and then apply your varnish.

If you've only just painted it, you can paint it darker. There are also ways to use an antiquing faux finish or glaze effect. Varnish is not going to darken, it's a sealer coat. Once something has been sealed, it's more complicated to darken it.

I would use a spray paint to darken it instead. Then seal it with a spray sealer made for outdoor use.

A dry brush with a little darker color would undoubtedly work if the set is painted. Consider using a gel stain over it if it's discolored; just make sure to clean it off completely before applying your varnish. If it's recently painted, you can apply a darker coat.

https://www.youtube.com/watch?v=TPvkaxQyQZ0