I have a dwarf Mulberry the tree is only a couple feet tall in a pot and producing tiny dark fruits that are very tasty. Got it last year from Logee's. I'm sure a web search will result in several nurseries that carry good productive varieties. I also have a couple "wlid" trees in my back yard area that are fruiting right now too. There is a white and and a couple darks. Last year I had a clump of them removed to allow for more sun in my yard. I am constantly fighting the seedlings coming up as weeds everywhere.

I have also loved them since childhood. We just had a huge one cut down. I hated to do it, but it was so tall there were very few I could reach to pick. All they did was make a horrible mess for two months. Luckily a nice sapling is already coming up from the trunk and I hope to keep it pruned to a reasonable height. 

Tony, happy to ship you some cuttings.  I'd export a couple of 30' tall trees if I could, they're ugly as hell.  The fruit looks more like what Bass shows above (the white ones), but they occasionally have a dark one here or there (fluke?).  Mostly are white.  Happy to share.  PM me your info, I've cut off more branches than I can count over the last several weeks.

I failed on rooting Mulberry last year and am currently trying Kokuso No. 20, Shangri La, Middleton, Geraldi Dwarf, and Pakistan again this year. I am trying a liquid rooting hormone this year, but I think I kept them too dry last year. I am a terrible rooter (is that a word?) even on figs, my success rate is pretty abysmal. On the Mulberry and Pomegranates I am trying to root I am putting multiple cuttings in a tall 5 gal pot, and so far Shangri La and Middleton look good, but the others are just breaking bud. I hope there is rooting going on underground. last year I show good top growth, but they faded as there was no root activity. Maybe those that have better success rooting mulberry can share their methods here. I have never tried the Sphagnum moss, baggy, or other methods we detail here on figs, and if that’s what it takes I will try it.  I grafted 1 or 2 of each cultivar to my Illinois Everbearing as well, and I believe they all took, but then a late freeze knocked everything back. Even the I.E. itself lost all the foliage and many small limbs. The tree itself leafed back, but the grafts had not leafed back 2 weeks ago when I was last at my planting about an hour away. At least the I.E. itself will make a comeback, which is more than I can say about some of my persimmon.

I grow a Che tree, it is not difficult to grow at all. Got mine from Edible Landscape after I saw Bass's tree. Mine is in a pot awaiting the day I can convince my wife to allow me to remove the apple tree in the front of our house so I can plant my Che tree. Sadly, in the pot, the fruit does fall off each year. As I understand it, that happens in ground too for the first few years. Also while we are talking about Mulberries I removed a small group of Mulberry trees last year to allow more sun in my yard for figs and veggies. My next door neighbor just had his cut down today as well. Yipee, more sun, less food for my tortoises though. 

Tony the tree guys ground it all up, but I've got tons more and tons of young trees growing everywhere as weeds. Not sure you would want this variety, it grows very big, fruit is ok though. Not a named variety just a wild Mulberry 

I had one in a pot that I was playing around with trying a little bonsai. I pruned it and kept it for over a year, pruned it again, it croaked and I moved on to other stuff. Don't know what I did wrong, these things are usually hard to kill. Maybe I went a little crazy with the pruning. If you really want a cutting, send me a pm. I can send you cuttings or possibly a seedling or 2 or both   

Still intending to send.  I have a pile of about 8 packages, plants, cuttings, etc. that needs to go out.  I've been expecting some slowdown at work, but it ain't happened in almost 3 months.  Can't handle the load much longer, so hope it ends soon!