Keep good notes?
Seriously, just use less water, until you have the correct proportions figured out. Trial and error is a long process, but I don't see any shortcuts in you case if you can't find a recipe already using brown rice and spinach. The extra water used in making brown rice should really be absorbed by the rice, the preparation shouldn't have too much extra water left in it unless there was a mis-measurement. The water added by the spinach has to be accounted for, but without knowing amount or preparation of spinach, or anything else there's no way to guess how much water would be added (and therefore how much needs to be removed to balance it out).
The recipes I found for Arancini (I I think this is the same thing, please mention if if you meant something else) - have the rice and other ingredients cooked risotto style first, rather than in a rice cooker or by some hands-off method that requires pre-measured water. In short, it means you don't have to get the amount of rice exactly right immediately, you can use much less water at first, and slowly add more if it's getting too dry, or even cook a bit longer to reduce if it's getting too wet. Longer cooking may change the texture a bit, if you aren't careful, but if you are gentle with the heat it may come out alright - especially since the recipe is going to be cooked again anyway to make the balls with.
If you are intending to have the spinach stuffed into the balls, instead of mixed into the risotto - then Joe's link will be useful, as you need to get as much water as you can out of the spinach beforehand (possibly you can still add it to the risotto), and there are limits in how dry you can make the risotto to balance the extra moisture. If you cannot balance the moisture even after pushing the spinach and the risotto to their limits, you may just have to use a different preparation of spinach, or lesser quantities.