Generally I favor changing the first engine oil at no more than 1,500 miles. Those first 1,500 should be driven easy as you are breaking in the engine and establishing wear patterns. Hard driving may see you chased by a blue cloud earlier than you like.
As there's no combustion in axles or transmissions I think the impact should be considerably lower, though it may not be a bad idea to change oil/fluid within 30,000 miles and then you can probably wait 100K for the next.
Seeing black gunk coming out doesn't sound promising. I wonder if your rear diff is running hot and turning some of the oil to carbon. If that's the case you'll be experiencing some serious wear. Should have that checked out.