First - easiest way is the one you say you have suggested to him -- and nothing will self-destruct if he types in his old e-mail address, then types in one guess at the password which turns out to be wrong.
Do not remember if one can sit there trying an unlimited number of times, or if after a certain number of times one needs to pause or whatever - but certainly would say he would lose nothing by trying any possibilities he can think of .
If he cannot remember his password - next question -- does Geni tell you no mail can go to his e-mail address and invite you to enter a new e-mail address for him?
If not - you might try sending him a message, and see if that triggers geni discovering that that e-mail does not work.
Believe if Geni has asked for a new e-mail address as above, and you give it -- then if he enters that e-mail address and says "forgot password" that they will send a new password to that e-mail address - then he can log in, make sure that is now his primary/only e-mail, and set the password he prefers.
At least, think it works that way - comment in Help from 2011 says back then it was not. But - it does give directions to change the e-mail once one has logged in, and the e-mail address to write to if cannot log in thru either of the above procedures:
https://help.geni.com/hc/en-us/community/posts/222038047-Need-to-ch...
- - Not sure which info you need to give, or if your cousin needs to be the one who wirtes, but if you write, include the URL of your cousin's profile, and if you were the one who originally added the profile, mention it. In the past, think what one got was Customer Service might then close the account, so you could then send a new invite using the currently correct e-mail.
(that is also basically what they say here: https://help.geni.com/hc/en-us/articles/229702907
again, info - this time with link to where to change e-mail and passoword: https://help.geni.com/hc/en-us/community/posts/222076727-Can-t-use-...