Before we go onto what colors might have been available, let’s talk about exactly what Joseph was wearing, a “kə·ṯō·neṯ pas·sîm”.

Ketonet is a bit vague; it means some sort of clothing. It’s generally translated as coat, tunic, robe, dress, etc. It’s what God makes for Adam and Eve in the Garden of Eden. It’s what Aaron wears as High Priest. Its what a variety of other priests wear. It’s what the princess Tamar (David’s daughter) wears after Amnon rapes her. It’s what the bride wears in Song of Solomon. In all cases it appears to be worn by someone significant or directly gifted from God. Of the 21 (non-Joseph) references, 14 are to priestly wear. And we never see it used to reference specifically “commoners” clothing. It seems to be specifically by nature a fancy piece of clothing worn by royalty, priests, or gifted from God. It’s not just a “coat;” it’s a fancy fraught with significance coat.

Passim is a bit of a mystery. It’s only used for two things in the Bible, once to refer to Joseph’s coat and the other to Tamar’s post rape dress. The Greek authors of the Septuagint translated it in Joseph’s story as ποικίλον (poikilos) or many-colored. In Tamar’s story they translated it as καρπωτός (karpōtos) or long-sleeved. So even for ancient translators weren’t certain. In modern Hebrew it means striped. There’s a whole bunch of argumentation about it. In addition to colorful, long-sleeved, striped, various authors have suggested thin, silk, patterned, embroidered, hooded, appliquéd, and probably others I haven’t seen. In any case “passim” seems to be providing emphasis to ketonet. It’s not just a fancy coat of significance, it’s a extra-special fancy coat of significance. Whether it’s varicolored, of specific pattern, specific fabric, or something else is impossible to say for certain. But let’s say varicolored seems possible and finally get around to talking about colors.

Ancient Israel would have had access to a large variety of colors from various sources. It’s harder to say what might have been available to Jacob/Israel (if he existed) so I’m going to focus on colors that would have been available to Israelites in the period Exodus likely would have been written somewhere between the 8th and 4th centuries BC.

• Madder. Madder is a collection of varieties of small woody flowers. Their roots can be used to make a whole variety of purples (maroons really) reds and oranges.
• Safflower. Safflower is a type of thistle that can be used to make a variety of pinks, oranges, and yellows.
• Woad. A flowering shrub. It can be used to make a variety of blues.
• Indigo. It’s not native to the area, but was imported in fairly high quantities. Like woad it created blues, but of a more vibrant nature, and it was more colorsafe. So even thought the locals had blues, true indigo was highly prized.
• Kermes insect. This oak parasite made a truly vivid scarlet red.
• Murex snails. Perhaps the most famous dye in history was Tyrion purple which made made in Phoenicia from certain sea snails. It was an almost iridescent reddish purple. In later times it became particularly associated with Roman emperors because of the brilliance and rarity of the dye.
• Tannins. A variety of fruits, nuts, barks, and woods were used as sources of tannins which produce a variety of yellows, tans, and browns.

So with a single pass of dye they had a wide variety of reds, pinks, oranges, yellows, blues, tans, and browns. And if you had just gobs of money you could get a rather spectacular purple. On top of these, they did know how to make multiple passes of dyes and could use it to make more distinct shades and could make cheaper versions of purples. Plus multi-pass dying was the one way they had to make color safe greens. Ancient color theory worked like modern color theory, and they weren’t shy about mixing.

So to sum up, if Joseph’s coat was truly a “coat of many colors” instead of a long sleeved coat, or striped coat, pretty much any and all colors could have been included.