I have a 2006 Corvette that produces a whining noise from the rear end when decelerating from 68-60?

Needs to be off the ground to see for sure. When it comes to differential bearings I replace all them, to include the axle bearings. Depends on the vehicle. No year make or model. the differential also needs looked at.

Did the noise start before or after the ring and pinion were replaced? Is it a whining or grinding noise?

noise when accel and decel means noisy gears on rear endcheck if the fluid is contaminated with metal particles meaning you need to do some diff repairs

The whining noise could be for many reasons. Narrowing the possibilities depends on when the noise occurs. If it happens only while decelerating at any or all speeds is most likely caused by bad pinion bearings or loose pinion bearing preload. If it happens during acceleration over a small or large speed range is usually caused by worn ring and pinion gears.

One cheap thing to check is the fluid level in the differential. If low, topping off the lube may help for a while.

I'm not a Euro guy- but how about
rear wheel hub bearings

Take it back to the mechanic that rebuilt it the gear set up is wrong and that is what causes the howl.

Here are the common causes or rear end noises
Constant high pitched whine at all speeds: Pinion Bearings or Ring gear carrier bearings
Whine at steady speeds or whines on deceleration: Rear end gear set is worn and will need to be replaced.
Rumbling type of noises are caused by wheel bearings or a tire with a separated cord.

Manufacturer : GENERAL MOTORS CORP.

Service Bulletin Num : 030417002 Date of Bulletin: DEC 01, 2006

NHTSA Item Number: 10001111

Component: POWER TRAIN:AXLE ASSEMBLY

Summary: WHINE NOISE FROM REAR AXLE. *TT
I just went through the same problem with my SS. It had 3000 miles on it and it was whinning while turning either left or right. I took it to the dealer and they replaced the entire rear axle. I am not the first person that I know to have this problem. I was told that there was a problem with some of the rear ends and I have had no further problems since having mine replaced.
Thank you for using Fixya and good luck

Well you can remove the sensor in the diff and make sure that looks ok they g obad quiet often also woulnd not hurt too remove the rear diff cover and inspect the rear end if it is whining and you dont see anything wrong i would refill it with lucas oil/grease and start praying check the pinion too and see if it has any play in it

Id get a mechanic to look at it. Sounds like a rear end bearing problem. Axle bearings pumpkin bearings.