What can you do to tan skin around a big birthmark ?

Sun effect: The reason the skin may not be "tanning" is less presence of melanocytes around birthmarks which would pick up sunlight. However, as a physician i would recommend sunscreen lotion and not actively tanning as it increases your risk of skin cancers.

Halo Nevus?: Skin around a halo nevus will burn, but not tan, as it lacks cells that produce melanin. This is the one appropriate use of spray tan, but only on that spot, and you still need sunblock. http://emedicine.medscape.com/article/1057446-overview.