Big, red, and German
When the portraits are in color, most of these rosaries are red, with gold or silver gauds. Red usually indicates red coral, extremely expensive both then and now. The gauds are at least as large as the other beads, and very often when you can see the whole thing there's also a pierced ball (a pomander, presumably) at least a couple of inches in diameter.
I've wondered for some time whether the beads were really that big, or whether the painters are exaggerating at the sitter's request -- the message being "Look what a big coral rosary my husband can afford."
It's certainly possible that actual rosaries of this type could have been made of imitation coral rather than the real thing. Imitation precious stones and glass "pearls" are certainly common enough in period examples. There's a practical limitation, however: a string of beads of glass or semiprecious stone weighs half again as much as the same size of beads in coral. A string of 16-20mm beads of this size could weigh 11 or 12 ounces (3/4 of a pound), which might be too heavy to wear comfortably. Coral is much lighter than stone because it's basically constructed like bone, with lots of microscopic air spaces.
These big red rosaries are so spectacular that I just had to make a replica. I have a string of dyed "sponge coral" 16mm beads, and one pierced silver bead, which I've strung into a version of such a rosary (pictured below). I pushed a little bag made of nylon mesh into the "pomander" and inserted small bits of clove, cinnamon and allspice that would fit through the bead's opening, then sewed the bag closed. So the whole thing smells a little like mulled cider :).
So far I've been unsuccessful at finding silver gauds in the right size range that look good and go with the pierced bead I already have. It appears to be from India, so I'll keep looking: I expect a really big gem show is what I need to find.