Of course you can use a big circle and a small brush to accurately apply the colours needed for your knife throwing target. Or you safe time by getting yourself a spray template.
The template you see laying in the grass in the picture is one that produces the typical EuroThrowers circle target - black centre, white, red, white, red. First you would spray the entire target surface in white, and then use the template to selectively add black and red.
Model making plastic sheets or plywood (thickness 6mm each) are the materials of choice for making the spray template. This last time, use your big circle to draw yourself the outlines, or send this DXF CAD file right to your laser cutting shop.
As for the spray paint on the target, be sure to let it dry overnight, or your knives will have some spooky red colour on the blade. After spraying, wipe the template clean with a cloth, and it will serve you accurately for years.
Many thanks to Alan K Parish of the Essex Backyard Throwers for providing the template photo and template CAD file.