It might be a good idea to use a baby acrylic - those are sport weight, and Bernat makes a lot that are readily available... but not in black :(
]KnitPicks has DK and sport weight cotton -which would be great as far as providing warmth, but not too much- but again, it doesn't come in black.
If you're feeling up to using smaller needles, you could try sock yarn... I think Knit Picks has that in solid black, and it would be just a bit smaller than sport weight.