I think you can extrapolate a lot of metaphors from "nurse." Two that I believe Emerson was going for are "to nurture" and "provide sustenance or entice." Emerson may have been describing schools mostly for boys with male teachers, so he could be expressing the need for a feminine touch to teaching. In any case, I think this line implies Emerson's plea for the need of a motherly affection between teacher and student.
"Nursing" connotes different things: nursing back to health, providing sustenance (breast feeding) and generally taking care of someone. "Genius" is, in this context more along the lines of creativity and potential. So, nursing this genius is to give it care, to feed it and; here's one that Emerson may or may not have implied: to entice. First, to entice in the motherly way as a baby needs and craves milk; simply, to entice with food which is necessary for life and, metaphorically, necessary to promote creativity.
In the context of the historically gender-stereotype of nurses being female and the nurse-patient relationship, this additional metaphor of enticing seems to have a slight sexual innuendo; not necessarily outright sexual, but within the discourse of enticing. One is enticed by food, sex, comfort, and encouragement. So the idea of enticement in general is simply a metaphor for encouraging, promoting, feeding and caring for that "genius." The teacher must not simply feed the student knowledge; but must entice the student; nurse his creativity. And thereby, with this motherly or historically feminine aspect to the more traditionally "manly" disciplinarian approach where the student is forced to learn the classics, the student is enticed, encouraged and feels a sense of affection. Thereby, the college has a feel that is more like "home."