Hmm. Thanks for the question and the link. Diakonie might just be the answer to how to translate 'outreach ministry'; cf.:
related discussion:outreach (noun)(Hope the link works; if not, 'outreach' in LEO should fetch the same thread. Unfortunately I wasn't able either to find it via Google or to access it directly via the alphabetical archive index in LEO, from which when I clicked on the exact same link, I got only the infamous 'most probably not [in boldface] Your [with a capital Y] problem' error message <deep sigh>.)
Technically, the cognate noun is 'deacon' and the adjective is 'diaconal.' However, in English these words both refer more normally to lay offices: in some denominations, elected lay leaders in a local congregation (along with elders, as in the early church); in others, members of an officially recognized lay order of ministry that requires a level of formal training and commitment only slightly below that of actual ordination as clergy (try a web search on 'diaconal ministry' or 'diaconate').
In referring specifically to the national church agency, you might want to just keep the proper name plus an explanation: Diakonisches Werk (the outreach ministry of the Lutheran Church of Germany). More general options might include 'church-sponsored community service,' 'outreach work of the church,' and so on. You might also be able to say 'through my volunteer work with...' (unless you were a paid employee).
Oops, good thing I F5ed. 'Charitable' is of course also fine. Perhaps a shade less PC because it can sound a little more condescending or old-fashioned (Dickensian workhouses, ladies taking baskets to sick peasants, etc.), but by no means obsolete.
'Diaconic' may be a word, but it's not in any of my dictionaries, including OED and W3.
I still think 'outreach' in this sense deserves a New Entry. One day.
