When they show an interest
I did Latin for one year at school, aged 13. I can whole-heartedly say that it has helped immensely through other education, not because those subjects use Latin, but because the 'lingo-lego' nature of Latin helps you to analyse/deconstruct other words, phrases and languages.
It helped with my Mathematics, Computing, French and Music at school and then has helped my Engineering and Business career in many (often intangible) ways. It helped me to learn (spoken) Chinese by myself, and to decipher Spanish, Italian, Japanese and Swahili phrases when I needed to. Understanding medical diagnoses has also been useful.
One of the challenges we had when learning was that nobody really speaks Latin any more. In the UK, you can see a whole lot of scriptures in churches, cathedrals, on monuments and many older buildings, so as a child, you could see it all over the place.
..but if you're not in a place where you see a lot of Latin around, it can be a tough call to motivate a child to take on a language that nobody speaks on a day-to-day basis. If you could find some interesting/cool audio or movies to help with motivation, that would be a plus. Our Latin teacher managed to find some Roman plays in nearby University theatres, which were huge fun.
If its offered at school, this would complement any tutoring you wish to give at home, so this would be an ideal age. Otherwise, it comes down to drumming up their interest, which depends on the childs' age and the numerous other distractions they have in their life.