Ansible 2.2.0 gained the ability to manage user units. It's not as straight forward as using the new user parameter though. Here is an example managing a per-user gpg-agent socket:

- name: user gpg-agent
  systemd:
    name: gpg-agent.socket
    state: started
    enabled: yes
    user: yes
  become: yes
  become_user: "{{ item.name }}"
  become_method: su
  environment:
    XDG_RUNTIME_DIR: "/run/user/{{ item.uid }}"
  with_items: "{{ users }}"

Without the XDG_RUNTIME_DIR environment variable set correctly you'll get the following failure:

failure 1 running systemctl show for 'gpg-agent.socket': Failed to connect to bus: Permission denied.

This example expects a users variable looking like:

users:
  - name: foo
    uid: 1000
  - name: bar
    uid: 1001