Currently the GEDCOM import page (http://www.geni.com/gedcom/start) displays the message "We are experiencing technical difficulties." This is misleading, because it leads members to believe that the problem is temporary and will be fixed soon, when in fact it has been over a year since Geni allowed GEDCOM imports. Therefore, you should change the message on the page to the one Monica Cruz has provided:
In the past we allowed users to import GEDCOM files onto Geni. However, this caused a tremendous amount of duplicates and cleaning up the Big Tree became a tedious task. Therefore, we have temporarily disabled our GEDCOM importer feature to prevent people from creating duplicate profiles.
You might first try searching for a Surname here or our Public Directory to see if any of your relatives already have those people included in their tree. If they do, you can easily reach out to them and merge your tree with theirs. Once you are merged into their tree, those profiles will also be in your tree and you will be able to access/edit that information.
If their profiles are not yet on Geni, you will be required to enter those people on the tree manually.