D.M.
You could have a princess spa party and invite this child. A slumber party is a good idea. Have this child bring a bathing suit and then she can have a bubble bath with your daughter. Then bring out pretty smelling stuff like lotions, perfume, and of course deodorant. Make it lots of fun, do her fingernails and other girly girl stuff. Explain the deodorant and why your daughter uses it; include the fact that one should take a bath first! You may not have to ever mention that she smells. The fact that the other kids use it to smell good may be quite enough. Send her home with a goody bag with stuff from the party and with her own special deodorant. Secret has some wonderful smelling ones that release smell when you heat up. This is the only way I can think of to do it with out offense. If she goes back to smelling later then have you daughter gently ask her if she used the deodorant and tell her how pretty she smelled when she used it.