The traditional way would be using groups. User Jenkins is added to the the minecraft-group (the corrosponding group for user minecraft). Then the minecraft-user gives the minecraft-group write-permissions for the directory in question (eg.
chmod g+w ~minecraft/some_directory). Of course it's also possible (for root) to create a custom group just be used with this directory (eg. a new group minewriters or something). If the minecraft-user is the administrator og the minecraft-group, he can add users to the group with
gpasswd -a user group (
gpasswd -a jenkins minecraft ) - else root must add users to the group.
A newer, better and more fine-tuned way (though a bit complex) is using Access Control Lists (acl), where the owner of a file or directory can give specific users and/or groups access to a file or directory. The minecraft-user would just add jenkins to the "access-list" of the directory in question, and give jenkins write-permissions to the directory.
setfacl -m user:jenkins:rwx ~minecraft/some_directory
This will give the user jenkins the right to create new files (w), list the contens with ls (r) and change into the directory (x).
Access to files and directories are somewhat dependent on the users' access to the directories above. If user jenkins can't enter the home-directory of user minecraft (/home/minecraft), then he can't access any directories under it either... even if he has been given permission with
setfacl to the particular directory.
So user minecraft must implicitely or explicitely also give user jenkins at least execute (x) permission to his home-directory (and all directories between his home-directory and the directory jenkins shall be allowed to write to). Execute permission for a directory, gives the right to "enter" the directory (eg. with the
cd command). Most user will also appriciate having read-permission (r) - which gives them the right to list directory-content with commands like
ls - so they can orient themselves.
If the permissions of minecraft's home-directory already is 'rwxr-x---' or 'rwxr-xr-x' (which is often is) that is enough... if it's 'rwx------' then access must be modified to give at least members of the minecraft-group - or user jenkins - access.
It's also a good idea to add the sticky-bit to the directory jenkins should be allowed to write to (ie.
chmod a+t ~minecraft/some_directory ). This prevents users with write-permissions to a directory from deleting files belonging to other users (with the exception of the directory's owner, which still may delete any files).