I have the best luck when taking cuttings at the end of December or very early January. Use a rooting hormone. A very old plant may be very hard to root. If you can access the base area of the plant, take the cuttings from that area. Don't take the cuttings from the outer edges of the plant. Those areas will be very mature and may be hard to root. On the plus side, this is a prostrate, creeping (I assume) juniper and prostrate junipers are much easier to root than the upright junipers, which can be almost impossible.
Good luck,
tl³

Thanks "treelover3" I thought I would take a cutting from most recent growth, which would be on the outside. So, just how mature should the cutting be?

Well, as a tree/shrub/conifer grows, the outer growth matures but the inner branches near the center of the plant remains juvenile. That's why you will see deciduous trees with leaves holding near the base/center of the tree while all of the leaves have been lost from the outer branches. The inner branches are still juvenile and so retain leaves. While the whole plant does age, only the outermost growth actually matures.

You want cuttings from this past year's growth and if you can get the cuttings from a part of the plant that is shaded, all the better. I find that cuttings from the shaded side of a plant root easier/better than cuttings from the sunny side of the plant. Take cuttings about 4" (10 cm) in length.