How do you say niece and nephew in Japanese?

They are, in the same order as above, 'mei' and 'oi,' written: 姪　甥
niece - 姪 (めい) mei, also commonly 姪っ子 (めいっこ) meikko

nephew - 甥 (おい) oi, also commonly 甥っ子 (おいっこ) oikko

I believe that the latter forms are more common because they're most distinguishable when spoken.