The easiest way to propagate blackberries is to tip root them.

It's a simple form of layering. Arch the growing tip back down to the ground (or into a pot) and hold it there in some fashion.

The portion touching the ground will form roots and then you can cut it free from the original and plant it where you like. They will naturally do this on their own if you aren't paying attention.

With black currants I've only taken dormant cuttings. I've simply trimmed off 6 inches or so stuck it in the ground. I think the first one I covered with a cut off milk jug or something like that to keep up the humidity, but I think I've also done it successfully without.

I think its worth a try. Here in Michigan, wild blackberies and wild black raspberries (we call them 'blackcaps' here) both grow in fairly wooded areas, not ultra dense shade, but definitely dappled sunlight at best -- probably similar to the conditions you described.

I have some gooseberries that have been in pretty dense shade under oak and aspen for a number of years. They are more whispy and open than the same variety in sun,but they survive and produce. Currant would probably be the same.

Worth a try I think. If they weren't producing, would there perhaps be a way to thin the tree canopy to let in a little more light?

Black currants or red currants? They differ in their sun requirements in my experience. Black currants are oK in areas with limited sun, but I never tried to grow them with just 1 hour of sun. With 3-4 hours they are fine. Red currants never produced well for me in shady location and the few berries you will get are going to be very sour.
Olga

I did as described above with Triple Crown, having purchased one plant in a 6" pot for what I thought was way too much. Now I have three plants!

Mine, however, are in containers between a fence and the south side of my house. This narrow space is shaded except during the "growing season" due to the close proximity of a house that grew a second story (and moved six feet closer) and a ridiculous tree planted right up against the fence. But...right now the plants looks really good, so time will tell how they like the cold shade of the fall and winter.

Oh, and containers because when I started working on the strip of soil I discovered to my dismay that there was a concrete shelf coming out from the foundation and also roots of the accursed tree from next door had begun to colonize the soil that was available (which means its roots traveled under the sidewalk--more to come, no doubt...).

Thanks everyone for your input.

It seems that tip layering is the way to go with the blackberry. Is there a specific season when tip layering works best?

My two blackberries have very different growth habits (both are in their second season). The Triple Crown has only one new cane growing this year, but it's as thick as my thumb and very vigorous. I also has one cane from last year that branched out and it will start flowering soon. If I understand correctly this old cane will die at the end of the year, so the tip layering only applies to the new cane. If so, I will probably pinch it in mid summer to force it make several laterals and tip root those. However, I do see a problem: it's so vigorous and the canes are so stiff that I doubt I'll be able to bend them to the ground. I wonder if air layering would work too?

The Black Pearl has many canes growing (5 or so) but they are very very thin (maybe 1/8") and almost no vigor. I will try to tip layer a couple of them to see what happens. Because of the low vigor it may not be a good candidate for the shaded area.

As for the currents - I only have a white one, also in its second year. It's supposed to be quite sweet if grown in ideal conditions, it has a few fruits that will probably start ripening next month. I can try rooting hardwood in winter, but I was hoping that if I root green wood this summer it will have more vigor next spring.

White current is similar to red, they are basically the same plant, only the color of berries is different. I would expect them need more sun

Yes - white and red currants are the same plant but black currants are not and they taste very different. I would ask how wide your bed is as a mature blackcurrant can be 4 -5 ft wide depending on the variety.

I imagine you can tip root even the cane with the buds on it right now. I don't think blackberries much care. I was doing my tip rooting during the fall and winter. In fact, after I had used the tip of a small cane, I cut that off to make a new plant, then pinned the next remaining node down to a new 1 gal pot, covered with a little potting soil, and voila! So they are not very circumspect.