Stainless Steel balls would work well.
But there are a LOT of different stainless steel alloys. The one I used for my fountain pen ink converters is #302, specifically for corrosion resistance. But according to the web, #302 is non-magnetic, so won't work with a magnetic stirrer.
The other problem is minimum order quantity. I ordered 5/32 inch balls, and had a 300 ball minimum order, and I have a LOT of left over balls. Minimum order quantity depends on the size of the ball and who you buy it from. The shipping and handling for only 6 stainless steel balls (from a commercial dealer) would likely be out of proportion to the cost of the balls.
If anyone wants 5/32 inch SS balls, I'm selling them for 6 for $1 + postage. Cheaper if you want significantly more than 6.
Although for a BOTTLE of ink, I think you would want to use something larger than 5/32 inch, maybe 1/4 inch.
@Alba
If the ceramic balls or marbles have enough mass, they should work. If the mass is not high enough, it will just get stuck in the thick ink, rather than mixing it. This is the problem with the plastic balls used in some fountain pen ink converters.