One rough effort at such definition would be: "any post-birth member of a species whose adult members are intelligent and conscious", where "birth" can be replaced by an analogous Schelling point in the development in an alien species, or by an arbitrary chosen line at a similar stage of development, if no such Schelling point exists.

Problem: There's no particular reason to expect speciation to be as widespread or as clear-cut as it is in the case of Earth and humans in particular. Certainly not for machine intelligences.

It might so happen that there could be software written for the computer I'm typing this on which could give it intelligence and consciousness. (Unlikely, but not out of the realm of possibility.) Should this machine be considered a person?

The reason I'm being so nit-picky is that what I consider the natural definition (namely, "an agent capable of intelligence and consciousness", or something like that) doesn't have this problem at all. I think it's a problem your definition has only because you were forced to deviate from the natural definition to include something that doesn't really seem like it belongs in that group - namely, newborns.