Cards for the Sick
This suggestion depends a little on the size of the organisation; it may be difficult to do in a larger work setting but is easier in a small organisation.
The idea is that, when someone is sick or off work, the Christian Group pay for and arrange a card, or maybe flowers if appropriate, to be sent to the individual. This may require some liaison with the HR element of the organisation.
Doing this allows the Christian Group to be seen to be expressing love towards the colleagues in the workplace - Christian or non-Christian alike. It also allows the group to help and bless the organisation, in a small way, by working with them to reach out to sick staff and make them feel valued and missed. This strategy may be attractive to HR and senior managers who hopefully will see it as an additional support for the organisation's pastoral care.