Catherine, just to nake sure you're aware of this: Your cousin's profile is marked as private. That means that only a small number of Geni users in her family group can see it. If your concern is that private information about her is being released publicly on the Internet, please be assured that it's not. The person who added her is likely another close relative who means no harm. Maybe it's someone you can work with to create a (private) memorial tribute to your cousin or with whom you can share happy memories.
I'm sorry for your loss.
Catherine ann Wegenka - I totally empathize with you. What happens is that you can report the profile as deceased. We just had a beloved relative pass away in March. There is an option on the drop down for all profiles that includes report as deceased.
I reported it in late April, asking that either Geni edit the profile as deceased or give management of the profile to our relative's daughter.
In your case, I believe that the manager that Yaacov mentioned can go into the profile directly and edit it. However you should report the profile in case that person is not on Geni frequently.
Private User - The problem that users experience is receiving birthday announcements about recently deceased relatives. I received one this morning for my deceased relative. That is why someone needs to report the profile to be edited as deceased, because it's hurtful.
Catherine Ann - I am sorry for your loss.