Do you mean a claimed profile? For example, when my cousin's mother passed away, we went to her profile to the upper righthand ACTIONS button and clicked to bring up the pull down menu. One option is to Report which in turn gives you various reasons to report, one being that the person is deceased.
Geni then quickly takes action and assigns as a manager the nearest active relative. You can add a comment on your report recommending who should manage the profile since sometimes the nearest relative calculation might be incorrect. So I recommended that my cousin manage her mother's profile.
Once Geni gets the report, they mark the profile as deceased and then the new manager can take actions such as add an obituary article, add the date.
If the profile you are talking about is not a claimed profile (managed by the person whose profile it is), then the manager can just go to Profile View now, click on Edit Profile and go into the relevant fields and values and change them.
If the profile have a "send message" link instead of a "contact profile managers" the profile is "claimed", i.e is a user profile, or at least bound to an email address.
To be able to mark such a profile as deceased you have to ask Geni staff to close the account first.
See instructions here in the FAQ: http://help.geni.com/entries/20470882-How-do-I-report-a-profile-as-...