[Lucid:]

I just looked through my items and the ONLY month that doesn't have both black and red on a single item from that month is September. USB Sword is Black, White, Blue. Inventor's Dream is Natural Brown/Crimson, Teal/Black, and .....uh, Brown/Weird Pinkish Color I Don't Recognize. Seabreeze is Sky, Blue, Teal.
Inventor's Dream pushes it a little, but since Natural Brown/Crimson and Teal/Black keep the Crimson and Black away from each other a bit, I'll count it.