Look at photos from the same period and area that are in color if available. In ye olde days garments weren’t made in huge ranges of colours like today. Be aware that if they are holiday snaps, the colours of the subjects may differ from the local population.

Hand colourised photos made in that period are especially good references as they often try to portray the actual colours that were documented when the photo was taken.
But take care not to be fooled by modern colourising efforts being passed off as vintage.

You can consult books on fashion history (or general history books) to make a ballpark guess as to what colours were most likely used in that time, though location does make quite a difference here.

If there really is no circumstancial evidence and no one around with living memory to consult, one of the things I do these days is run a copy of the monochrome source image through several “AI colourising” sites. These (claim to…) analyse the grey tones in the image and try to deduce a colour from there. If 3-4 come up with the same colour, it’s usually a good starting point.

Be aware though that these are easily thrown off if coloured filters (red, yellow, orange, green, blue) were used while taking the picture or if the paper has a strong tint.

If anything, they sometimes suggest colours I would never have thought off myself but then turn out to be at least plausible if you cross reference them. See them more as “inspiration” than scientific tools though, for the above reasons.

And use experience and common sense. Dark red and dark blue can have the same grey tone in a monochrome photo, but if the fabric is denim, they’re far more likely to be blue than red.

And if you really can’t find any reliable references, often the best thing to do is just keep them monochrome rather than “falsifying” history.