It translates to Dagobertian (the adjective to the first name "Dagobert") - just like "Edwardian" denotes the era of "Edward".
This doesn't help you much as a direct translation. You need to take into account that Scrooge McDuck, the impersonation of pure immense wealthiness, is called Dagobert Duck in the German translation of the Walt Disney comic - The adjective is used here as a tongue-in-cheek description for an era that swept a lot of financial and other support into the churches.
So, a very literal translation of your sentence would be along the lines of
When soon the wealthy and closely ecclesiastically tied generation of baby boomers will reach pension age, the Scrooge-McDuckian epoch of church history could abruptly come to an end, financial experts warn.