colcol,
Performance is variable - what works best for me here in southern KY (Illinois Everbearing) is not what is most productive for my buddy in Flint, MI. 'Mileage may vary, depending upon your location.
That said, my personal preferences are 1)Illinois Everbearing - a M.albaXrubra hybrid with vigorous growth, fruiting over a 6-8 wk period from early June to late July(here), with a flavor that has a good balance of sweet/tart; to me, it's the 'gold standard' - though some attribute that to M.nigra.
2)Stearns - another M.albaXrubra hybrid
3)Collier - another hybrid.

I would anticipate that all three of the above would be sufficiently hardy to do OK for you once they're established.
Sources? I'm not sure - check Burnt Ridge Nursery, Hidden Springs Nursery, Edible Landscape, Raintree, OneGreenWorld, etc.

The species red mulberry is a native, hardy from zones 5-9, native range is open woodland, clearings and roadsides, from MA to MI and south to FL and TX. So you are out of the natural range, but I see no reason why it shouldn't grow for you if the hybrids won't.

Probably if you Google you will find sources - try edible/fruiting trees, as well as mulberries...?

M.rubra is somewhat difficult to find in commerce, but it can be had. Fruit quality is good to great - I've never sampled an M.rubra that I didn't like.
OIKOS Tree Crops is offering paper pot-grown seedlings this year, Possibility Place Nursery has offered it in the past, and I suspect that ForestFarm &/or Woodlanders probably also offer it. Some of the commercial forestry nurseries(Cascade Forestry Nursery, Lawyer Nursery, Musser Forests, etc.) may have M.rubra available.
Some state division of forestry nurseries propagate and make M.rubra available - I recently saw that the NC DoF Nursery was offering M.rubra seedlings, while helping someone in NC who was looking for a source for significant numbers of M.rubra seedlings.

Thank you very much for the replies.
I've decided to try a red mulberry from Forest Farms
and a white mulberry from Raintree.

Colcol,
If you're looking at the white-fruited M.alba from Raintree, you might want to re-think that.
I'm not a huge fan, overall, of the introduced, invasive alien M.alba to begin with - though it does provide me with plenty of free rootstocks to graft superior fruiting selections onto.
But, I digress. The white fruited selections I've had opportunity to sample are just...blah. Almost flavorless, or at best, a 'grassy' flavor with a little sweetness. A friend had one that tasted sort of like muskmelon. Even the birds don't bother much with them if theres a good lavendar/black-fruited tree anywhere in the vicinity.

Musserforests has both M. nigra & rubra, but there's a min of 5 each & they're very small thru mail-order.

Here is a link that might be useful: Black mulberry at Musserforests

Can Morus Nigra survive in zone 6?

There is a local nursery here selling 1" caliper fruiting mulberry trees labeled "Persian Fruiting Mulberry morus nigra". At first I scoffed thinking that they were selling something that had no chance of surviving here, but after some looking online now I don't know.

Some web sites like the one linked above say morus nigra is hardy to zone 5, while many other suggest hardiness only to zone 7 or 8. What is the truth?

I looked at the California Rare Fruit Growers pages and they say that morus nigra will begin being harmed at 5 degrees and killed at 0 degrees.

We rarely drop below 0 here, but we do have late frosts. Would planting a morus nigra in zone 6 be a death centence or would 0 degree weather for a few days simply result in a few branches dieing back?

The other question is I am pretty sure this morus nigra for sale is grafted, probably only white mulberry root stock. The graft, I think, is about 5 feet high. If temperatures did drop below zero for a day or two would it cause the graft to die leaving a regular old bland white mulberry. Would planting a morus nigra next to the house offer it enough protection?

I have a very small Illinois everbearing mulberry that I ordered this spring, but the idea of getting a morus nigra to grow is very appealing.

I asked this question in the fruit and orchard forum, but have not received an answer yet.

Here is a link that might be useful: California Rare Fruit Growers

lucky_p, thank you for the reply, I appreciate the comments. I'm hoping for a real hardy tree & bird food. There aren't berries around here (near our farm), so I'll be curious if I'll get to sample any.

barclajo, I haven't researched it, but offhand, I think M. nigra should be perfectly hardy in z6. Prb'ly OK in z5. Native to the mountainous regions of Iran & the Caucasian Mts.

Stark Bros carries Illinois Everbearing Mulberry (hardy to zone 4).

Here is a link that might be useful: Illinois Everbearing Mulberry