Jake, if it were me, I'd probably either try blending my own from Tamiya red and brown, possibly with other colors, or adding artist's acrylics to red or brown Tamiya acrylics. But I once made part of my living by color matching paints, and I know enough about paints to avoid any problems this could cause. For others, it might be best to start with a Tamiya acrylic that looks closest, and blend with other Tamiya paint. It's best to go slow—3 drops of base color, one drop (or less) of the modifying color, let dry and match. The colors used to modify the base color (a dark red) should be dark brown, blue (not black), and a medium to dark yellow. The closer you can find a starting color to the finish color, the better.
If you decide to try this with artists acrylics, remember that they are concentrated colors, and you will need to increase the solvent, and may need to increase the binder. You can use Future for the binder, which will increase the gloss of the final product, but many bricks have eggshell to semigloss surfaces, anyway.
Something I'm going to have to try, sometime: using Future as a base and blending it with artist's acrylics. If it works, it opens up a whole range of possibilities.