Yes, most notably the F-16, which had a really good four-channel redundant analog flight control system. But is that needed on a transport aircraft? Fighters have it for extreme maneuverability, which a transport aircraft does not need or want.
Transport category aircraft are inherently stable by their aerodynamic design, it's a certification requirement.
If you have normal wings and the right size horizontal and vertical stabiliser the basic design of an aircraft is self stabilising. Especially with the wings sloping upwards (as all airliners have) because that wing shape also contributes to stability.
Never flown one, but as far as I know that's only moving the center of gravity by moving fuel. The CG is very important to inherent stability, if it moves behind the center of pressure you lose all pitch stability. And for efficiency you want it to be as far aft as possible because that reduces drag from the tailplane.
As a side note: Early relaxed stability planes had no software. It was implemented with analog computers