This was a relatively simple puzzle and lots of people answered correctly. First one to answer correctly was Anisha, my elder one (aged 10), though she had the benefit of getting the question at the time I was posting it. Prasanna Raghavendra, Anirudh & Anvi from Singapore, Vivek Shah, Sanjiv Gupta and Swati Bhargava in that order were the other ones to send correct answers. Well done and thank you all!
The best articulated answer came from Anavi Baddepudi (who I think is also a 10 year old from Singapore), and I am taking the liberty of reproducing her answer verbatim:
The answer is that both of them were lying and the black- haired is the girl where as, the red haired is the boy.
In the case that only the red haired child is lying, that means that he is actually a boy.. But that would also mean that the black haired child is a boy too, and the question states that there is one boy and one girl..
This is the same if the black haired child is the only one lying.
So this proves that both are lying.
Hence, the black- haired is the girl where as, the red haired is the boy.
Hope you enjoyed the puzzle!