From subjective experience so far and what I've picked up elsewhere, I'd gauge:
1,000 repetitions until a new movement feels somewhat comfortable
100,000 reps (so 100 x 1,000) until "good"
Min 1 / week (would assume otherwise you'd lose "it" plus any momentum)
Ideally daily, maybe even multiple shorter sessions during the same day for more effective learning
1 day / week break
You can always mix conscious practice into the day-to-day, however for a dedicated session something between .5 and 1.5h might strike a good balance between being worth it and not getting tiresome or straining.
The good thing about coordination and motor skill exercises vs strength, power, endurance: 1) you can always do something, even on an off-day, 2) that'll likely last.
Examples for triangulation:
* Brushing teeth with the other hand took me about ~5 years (= ~3650 sessions) to feel somewhat natural :)
* Juggling with the weaker hand ~1,000 * 100 = 100,000 tosses, so you could get to "good" in about a year.
* Forehand with the weaker hand ~100,000 swings including ~20,000 contacts
You'll likely have an S-shaped learning curve, i.e. slow start, then steep progress, and at some point diminishing returns.
If you get stuck along the way or experience setbacks, search for and switch to something else that might help (with cross-benefits) and then go back later.
Once you clearly hit diminishing returns, you're somewhat ironically back to why you're started on something new in the first place, so in the overall spirit at that point it's time to add variation or look for the next thing.