Yes, they'll dye.
Have you ever washed them ? or do they state 'dry clean only' ?
If it's the latter, then the cleaners might dye them for you. They'll charge you right enough, but they will do it.
If they wash fine then all you need is a dye that states that it 'will' dye wool. If it doesn't say it on the pack, then it won't. Wool needs an acid dye.
That said, the little Dylon home dyes work well, but you need a pot big enough to allow the garment to move freely in the dye liquor.
Wash in dyes a brilliant
even if you do need to wash out the washing machine with a few empty washes afterwards.
If you haven't washed them and don't know if they will shrink (they shouldn't, but we have no way of knowing how the fabric was fulled once it was made) then it's a hit or miss an up to yourself whether you risk it or not.
cheers,
Toddy