I just got this small stone bowl for $5 and its some kind of banded agate or something, but I want it to have a nicer patina, its kind of a cheap shiny looking thing right now, what are some ways I could give it different patinas and maybe even smooth out the stone where it gets a little rough?

I know a rock tumbler would probably work, but I just dont have the money for one right now, looking for DIY at home ways