That's actually an interesting idea - Discover issuing it as a premium card to give AmEx a run for their money. With all the AmEx fails lately, timing would almost be perfect.
What I would do is put absolutely zero reference to Discover on the front, just a small logo on the back of the card. Run it over the Discover network here and DC overseas like mentioned. Live person answer without pressing anything to speak to someone. US call centers 24/7. APPLE PAY FOR THE LOVE OF GOD. A good, solid mobile app like Discover already has (I feel Discover has the best mobile app, hands down, in the cc industry). Keep chip & pin. Keep it zero FTF. Travel related bonus categories.
Am I asking too much?
I think that trying to revive a dead brand (well, nearly dead) for the sake of nostalgia in a very small group of people is kind of a dead-end business idea.
If you look at the people who post here who are interested in credit cards, which in and of itself is a small subset of the population in that nearly everyone has a credit card but most people don't care too much about it as long as it's Visa/MasterCard/Amex/Discover and maybe pays them something back, and then you look at the subset of that subset who are interested in having a Diners Club card (again) it really becomes a small market.
While Discover or BMO could rise Diners from the dead you'd have to ask yourself what the benefit really was. I think Discover already has a premium card (Discover More - or something else). If not, it'd probably make more sense to build on the Discover brand than trying to resurrect the Diners Club brand. I think people would understand a credit card name like "Discover Select" as something new and geared as a premium credit card over Diners Club which would invoke more thoughts of, "Who uses Diners? I think my grandpa used to have one, back in the 1970s."
That being said, I like that Discover keeps their offerings limited. Right now I know of Discover It, Discover Miles, and I think there's Discover More. There may be one more but you can easily talk and discern the differences between them.