I've been saying they're "fairly common" for the wives of prosperous burghers in the 1500s, but exactly what evidence do I have to back this up?
Here are some of the ones that first caught my attention. (Clicking on each of these takes you to the 600k original photo at Bildindex):
All of these are by Bartolomaeus Bruyn the Elder (1493-1555), from Köln (Cologne), who painted at least twenty portraits of this type (not all with rosaries). The Cranachs and other contemporaries also painted portraits in this style.
Quite a few of them, like the first one, are pairs of portraits of a husband and wife. Some of these are probably betrothal or marriage portraits, especially if the people shown are young, or holding rings or flowers. Others may simply be tokens of middle-aged economic success.
Here are more of the Big Berthas.
I just found this one (1536, painter unknown):
This one is by Joos van Cleve:
Here is an unusually late one (1632) by Christiaen van Couwenbergh, whose usual portrait style is quite different. Seemingly this was a client who wanted something old-fashioned:
And for amusement, here's one being held by a doll!