If the vest is 100% wool, it can probably be dyed black. However, the dyeing process requires hot water, which will probably shrink the vest. It is best to dye wool items before sale, so that shrinkage does not render the garment unwearable. This sweater vest might be suitable only for a much smaller person after you have dyed it.

The most difficult and expensive aspect of dyeing wool clothing is that you will need a dyeing pot. This pot has to be large enough for the garment to move freely when stirred in the dye, as you heat it. It must not be made of a reactive material such as aluminum or iron. Only stainless steel or unchipped enamel will do. This pot will be a significant investment, because you can't just use a pot that your family uses to cook food. Textile dyes, including Rit dye, are not safe to use in cooking pots; once you have used a pot for dyeing clothing, you should not reuse it for food. A five-gallon or larger dyeing pot made of stainless steel will cost perhaps $100, which is probably more than you'd spend to buy a new sweater vest.

If you happen to have a suitable cooking pot to use, which will not need to be reused for cooking food, then you can consider the question of dye. The very best dye for hand-dyeing wool is Lanaset dye. It's very hard to buy this dye locally, but easy to buy it by mail-order from a good dye supplier. The black Lanaset dye is very rich and black, and, unlike most other dyes, it will not wash out in the laundry, even if you use hot water. The next-best choice, at half the price, is Pro Chemical & Dye's WashFast Acid Dye in Jet Black. The worst choice is an all-purpose dye such as Rit, but even this will work, if you use two to four times as much dye as the package instructions require, and add six tablespoons of white vinegar to every gallon of water you use in your dyebath. (That's 100 ml of vinegar in four liters of water.)

To dye the sweater, first dissolve the dye in hot water, then let it cool. Add the vinegar or other auxiliary chemicals require in the dye recipe. Place the wool vest in the pot and stir very gently as you gradually raise the temperature of the wool to almost boiling. Continue to stir very gently and hold this temperature for half an hour or an hour, or as indicated in your dye's instructions. Then let the dyebath cool gradually to room temperature, and rinse out the excess dye as indicated in your instructions. You must avoid sudden temperature changes or careless rough stirring, because either of these will tend to make your wool turn to felt.

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[This answer was first posted, by me, on Yahoo answers, on October 12, 2008.]