Are men and women permitted to shave pubic hair during sefira?
(Obviously only regarding a situation in that it is already permitted for the subject to shave his/her pubic hair during the year)
The rule applies to hair anywhere on the body (Nit'e Gavriel, Pesach volume 3, chapter 49, paragraph 2, page 279; see that chapter for exceptions, but pubic hair is explicitly not excepted).
Sephardic authorities such as Rav Ovadia Yoseph require women to shave their pubic hair prior to immersing in the mikvah. A woman who follows this practice may certainly shave her pubic hair if she needs to go to the mikvah during sephirah.
The prohibition of a man shaving his pubic hair derives from the assumption of Chazal that shaving pubic hair is the way of women and for a man it is prohibited from the pasuk (Devarim 22:5) "Lo yilbash gever simlas isha" "A man may not wear female clothes". Rashi there gives two explanations, the second of which is that a man must not remove his pubic or underarm hair. The word he uses is not shave, it is lo yasir, do not remove. So whereas a depilatory is permissible for a man to use to remove his beard (and vastly preferable halachically to using a shaver), seemingly he should not use it to remove underarm or pubic hair.