Also, often the context or the cousin's name will provide a clue to gender, but as Piscean has mentioned, English doesn't normally bother with the distinction that other languages may make.
Czech also has separate words for a male or female cousin. Some languages even differentiate between relations from your father's side and your mother's side. Arabic for instance, distinguishes between paternal and maternal grandparents, and even male and female paternal and maternal cousins.
I have a few Burmese students, and I was unaware it made the distinction. I'm glad to have read your post, as I learned something new.
Kyawwin, you list your native language as Burmese - do you happen to know if this male/female cousin distinction also exists in some of the other languages of Burma, such as Arakanese and the Karen languages?