Without the ability to use sudo your options become limited to essentially 2.
Method #1
You can either put the users into the same Unix group (/etc/group) so that they're able to access the same files & directories.
Example
$ more /etc/group
somegroup:x:1001:adminuser,nobody
You then need to set the parent directory that contains this file like so:
$ chgrp somegroup parentdir
$ chmod g+rwxs parentdir
This method will force any files or directories created underneath parentdir to have the group set to somegroup. This method works fairly well, by in large, but can be a bit fragile if parentdir's permissions or ownership gets messed up. Also this method doesn't work if files and/or directories are moved into the directory from some other location.
Method #2
The more robust way to do this would be to make use of access control lists (ACLs) on the file or directory of interest, using the command setfacl.
$ setfacl -Rdm g:somegroup:rx somedir
$ ll -d somedir/
drwxrwxr-x+ 2 saml saml 4096 Feb 17 20:46 somedir/
You can then confirm that the ACL has been applied using getfacl.
$ getfacl somedir/
# file: somedir/
# owner: saml
# group: saml
user::rwx
group::rwx
other::r-x
default:user::rwx
default:group::rwx
default:group:somegroup:r-x
default:mask::rwx
default:other::r-x
Setting the permissions above on the parent directory will enforce that a default ACL will get applied to any new files or sub-directories contained within somedir.
References
