The obvious way isn't possible because you don't have a neutral at the top of the stairs.
There is a way, but it involves a bit of lateral thought and a change in how you switch the lights.
You rewire so that your black/white/red cable becomes live/switched live/neutral.
You then have two single-way switches in parallel across live and switched live. You can wire a light from switched live and neutral at the switch at the top of the stairs.
Now both lights will work when either switch is on. Problem - you won't be able to turn the light off from downstairs when you've turned it on upstairs. You need a switch which will reset itself automatically when the light is not needed:
- time-lag switches as used in blocks of flats (UK pneumatic type shown, electronic equivalents are available) which will operate for a set period.
- passive infra-red detectors
which will operate whever motion is detected.
The two time-lag switches are wired in parallel with live/switched live/neutral at both switches, and the lights between switched live and neutral.
An added advantage of PIR detectors is it leaves your hands free if you are carrying things down stairs.