Late fall or early winter is an ideal time to take cuttings. More detailed info is included below with a link to the source article. However, if you would prefer to buy new plants rather than propagate them yourself, it shouldn't be too hard to find them, as 'Grey Owl' is still a readily available juniper cultivar in the nursery trade.

Here is link to article which discusses propagating Juniperus virginiana from cuttings:

https://plants.sc.egov.usda.gov/DocumentLibrary/plantguide/pdf/pg_juvi.pdf

The article states:

Propagation from Cuttings
Cuttings are made 5 to 15 cm (2 to 65 inches) long
from new lateral growth tips stripped of older
branches. A small piece of old wood, "a heel" is
thus left attached to the base of the cutting. Some
propagators believe this to be advantageous. In other
cases, good results are obtained when the cuttings are
just clipped without the "heel" from the older wood.
Cuttings from the current season's terminal growth
also root well.
Cuttings to be rooted in the greenhouse can be taken
at any time during the winter or rooted outdoors on
heated beds. Exposing the stock plants to several
hard freezes seems to give better rooting. Optimum
time for taking cuttings is when stock plants have
ceased growth (i.e. the late fall-winter propagation
period is more successful than summer). For
propagating in an outdoor cold frame, cuttings are
taken in late summer or early fall. There may be
advantages to using bottom heat. Lightly wounding
the base of the cuttings is sometimes helpful, and the
use of root-promoting chemicals, especially IBA, is
beneficial. Recommendations for root-promoting
chemicals include the following: 2500 IBA Quickdip (Alabama), 3000 ñ 8000 ppm IBA liquid, and
0.3-4.5 percent IBA talc. Medium-coarse sand or a
10:1 mixture of perlite and peat moss is a satisfactory
rooting medium. Maintenance of a humid
environment without excessive wetting of the
cuttings is desirable, as is a relatively high light
intensity. A light, intermittent mist can be used.
Bottom heat of 60-65°F (12°C) is critical the first six
weeks of propagation to allow the basal wound of
cuttings to callus.