Calculating with m/s$^2$ is very helpful when dealing with acceleration on the human range, as accelerating from rest at 4 m/s$^2$ for 3 seconds will give a velocity of 12 m/s. g is also a very helpful referent, as it describes the acceleration we are used to feeling.
For interstellar trips, the obvious unit choices would be light-years (ly) for distance and years (yr) for time, which would mean that acceleration would be in ly/yr$^2$. 1 ly/yr$^2$ is conveniently close to 1 g, and both are close to 10 m/s$^2$, which is nice. However, accelerating at 1 ly/yr$^2$ for 2 years does not result in a velocity of 2 ly/yr (as that would be faster than the speed of light, which is 1 ly/yr). While there are relatively uncomplicated formulae that result in the correct answer, the format of l y/yr$^2$ seems intuitively incorrect if it cannot be easily manipulated (indeed m/s$^2$ suffers from the same issue at such scales as well).
Is there an alternative way of expressing or formatting acceleration that, while perhaps appearing more cumbersome, better captures the effects of prolonged acceleration on velocities approaching the speed of light, and allows manipulation? I could not think of one off-hand, and have no reason to think there is, but I figured no harm in asking.