I'd give it a doing with Fiebing's leather dye, dark Brown.
Being for leather, it will soak into almost anything, and has a nice rich reddish colour.
It was my old pal Ron Ehlert first told me about this stain, and have used it a lot ever since. It will likely go on over what you have there already. Just let it soak in and dry a day or two before oiling. You can however, take a cloth and rub off the excess after a few minutes.
Hope this helps.
Richard.