Like almost any big-ball-of-mud exercise -- and research libraries have several of these on the books, from scholarly communication to research-data management to DH/DS centers -- success hinges on clearly defining success criteria up-front. There is no single, foolproof recipe for a "successful digital-scholarship center," and defining success as "success" (which happens all too often) is of course tautological tail-chasing.
What Emory is doing so extraordinarily well (and I was at that CNI presentation and am glad you cited it) is systematically answering the question "what do existing centers accomplish, and how much of that do we want to emulate at Emory?" Unsurprisingly, they found different answers at different centers. Some are explicit about being (and helping) grant-chasers. Some are just as explicit about being collaboration spaces, or tech and project-management support. Some are dev centers. None of these accomplishments is intrinsically more worthwhile than any other! They're all good! So for new centers looking for what to do, it's all in the goal-setting and assessment-planning.
If I were in your shoes, I'd interrogate that "growing need" and set goals based on it, preferably without even invoking the "center" concept -- I find that prematurely reifying a service leads to unhappy results. So...
- Digital folks having trouble getting grants? Why, and what can the library do about it?
- Everybody complaining about space? What could the library free up?
- Missing tech? Could the library purchase and/or host and/or support it?
- Missing skills? Who in the library has those skills and can teach them?
- Missing support structures? What could the library fill in? (This is a particularly common problem among grad students, I find.)
Be frank about this. If the real problem is "digital {whatever} is sexy and we're jealous," then that's the real problem; dancing around it because it's kind of a dumb problem won't help.
Now, stepping off my soapbox to return to your actual question, it seems to me that several of the centers you list started as idiosyncratic fiefdoms designed by and/or around one or two very bright and energetic people. So another way to tackle the planning process is to look around locally for the right horses to bet on, building an infrastructure around their needs. This is risky (good academic racehorses have a habit of switching stables), and it can be politically unpopular in libraries with a "must serve everyone equally" orientation, but it certainly simplifies determining assessment criteria! It may also endear the library to university administrators looking for ways to keep and/or poach "top talent."
tl;dr version: I don't know what a successful digital-scholarship center looks like; I believe they come in lots of shapes and colors. I DO know what an unsuccessful one looks like: a vaguely-conceived, under-resourced, unassessed bandwagon-jumping exercise run by one isolated low-totem-pole employee from a broom closet.
A digital-scholarship center that's not that has a tolerably good chance of doing something useful.
