I've found that using tea to dye fabric works quite well. Buy the largest box of cheap Tetley tea bags you can find and brew a pot using all the bags. It makes a great dye and even leaves a pleasant aroma to the fabric. I haven't tried it with my Tilley T3 but I don't see why it wouldn't work. I've had my Tilley for 21 years and it's still going strong, BTW.
Another option is to go to a craft store and pick up a fabric marker. They are specifically designed to color fabric and from my experience, they work really well. I used a black fabric marker to color a 100 denier Cordura backpack. It worked like a charm.
Another option is to go to a craft store and pick up a fabric marker. They are specifically designed to color fabric and from my experience, they work really well. I used a black fabric marker to color a 100 denier Cordura backpack. It worked like a charm.