Both nasciturus and nascendus seem to exist. Words ending in -turus are often described as future active participles, and words ending in -ndus as future passive participles (they are also called gerundives), but as nascor is always an intransitive verb, it doesn't seem like it could have any truly passive forms. (I think this differentiates nascendus from examples like patiendus, discussed in brianpck's answer here: How do I use gerundives of obligation for deponent verbs?)
I would guess that there is a difference in meaning something like "about to be born" vs. "needing to be born", but I don't understand the Latin participle system well enough to be sure.
I found a passage in Ars by (pseudo?) Palaemon that mentions the two forms, but my Latin is not strong enough to extract any information about potential differences in meaning or usage between the two forms:
futuri temporis participia a passivis vel communibus semper in dus. nam deponens numquam habet duo futura: nec enim dicimus 'luctandus est ille' aut nascendus, sed habet unum, ut luctaturus nasciturus locuturus; licet apud veteres talia quoque communis generis reperiantur.
("De Participio", Ars [sp.], in Keilor 1868, 546.9-13, accessed via PHI Latin Texts)
I also found an interesting but not very enlightening anecdote about a poor gentleman who shared my confusion and was excoriated by a bishop (The Downside Review, p. 228). Basically, all this does is confirm my understanding that both nasciturus and nascendus are valid forms. The bishop brings up the “ad homines nascendos vim hujus numeri (septenarii) pertinere ait” quote that is also mentioned in the Lewis and Short entry for nascor; L&S say that it can be translated as "to the formation of man in the womb".
Searching for the text of this passage also led me to a section of Roby (1875; A Grammar of the Latin Language from Plautus to Suetonius, Part II) that discusses this use of the gerundive. This was more helpful. Roby says that there are "very few" exceptions to the rule that the gerundive is passive, and therefore not used for intransitive verbs; he lists some examples and says "three of them are from Varro; they are all expressions of the same nature and all from verbs in -sc-" (p. lxx).
The examples seem to go against my guess that the gerundive would have a sense of obligation in this context; Roby translates them with phrases like "of the X-ing of Y". After reading Roby, I have the impression that even though nascendus isn't 'wrong' per se, there wouldn't be very many situations where I should use it. Does anybody have any further advice or information about the use of these two participial forms?