Colours question

One option would be to use car spray paint. You can get aerosol cans to touch up scratches from motor stores or online - search for "touch-up paint".
To get the best result you'd need to clean the metal well and use a primer and undercoat first, and after the colour coat use a hard gloss top coat (or even a metallic sparkly one if you fancy that).
Car paint is really hard wearing and durable, so given careful preparation and application I'm sure it'll be suitable and more than durable enough for use next to skin and clothing.

 

HT offers custom made color, as far as I know, Steelworks and BAW offer colors as well.

 

Embed an image of it and we may be able to find a pink one.

Also FYI, if you're after the material properties of metal due to allergy related reasons, it's inadvisable to paint it with just any spray paint as paints can have toxins that may slowly diffuse into the bloodstream, although that being said the stainless steels that most chinese manufacturers aren't the most superb quality either. Stuff like this matters if you want to wear a device permanently.

There are also alternates to painting, for example as an overkill method if you have all the time and money in the world and the skills, you could get a high vacuum system and a strong ioniser that vapourises something on a nanometre level to could coat the cage in something to give it a pink iridescent due to the thin-film effect. That's some next level engineering bullshit though and wouldn't exactly be durable.