It's generally recommneded that you use an analine dye. I'm building a kayak and have stained the hull a dark forest green.I got the dye from this site and I'm very pleased with the color.

https://www.toolsforworkingwood.com/store/item/LW-WCON.XX/W._D._Lockwood_Water_Based_Concentrated_Dye_Family?searchterm=forest%20green%20dy

They have a good selection of color and I can tell you after buying 2 1 oz packages that a 1 oz pack will be more than enough.

From the Rit Dye FAQ page under "What WILL Rit Dye?" :

Unfinished wood and wicker: furniture, picture frames, moldings, shutters, wicker baskets, straw, rattan and sisal squares

Laszlo

Yes you can use it but I highly recommend using something that will be more permanent when used to color something that will spend much of its lifetime outdoors in the sun.

RIT is fine for some fabrics but - despite their recommended uses described in Laszlo’s post above - there are more stable alternatives out there for your intended use.