In this answer to another question, solar system-scale rail gun acceleration (and deceleration) was brought up as an alternative, and I found this intriguing. It's worth another question at least.
In a mass accelerator (rail gun), an object is drawn through a ring using an electromagnet, the ring is turned off, and the accelerated object heads off to the next ring for another boost. In space (essentially zero gee), this would mean that the object would experience acceleration while it was within the range of effect of the ring and coast between rings.
I understand the inverse square law, where $ I = 1/r^2 $, however I don't understand how that relates to how well a giant electromagnet ring is going to effectively pull on an object (say 100 tonnes) that's moving at some fraction of $ c $ toward it. Each successive ring is going to have less time to pull on the object, and thereby the speed gain incremental is going to be smaller each time.
Presuming you could get a powerful enough magnetic ring to do the job, human passengers could stand high $g$ acceleration for brief periods of time ($10g$ for several minutes, $2g$ for 24 hours). If the average effect time from the Acceleration Range problem above were one second, I presume each ring would only add 9.8 m/s to the speed, which means it would take a lot of rings to get up to a useful fraction of $c$.
Number of Rings
So, how many rings would it take to accelerate an object to greater than $.5c$? How about $.7c$? How much acceleration time would each ring have on the object? Let's put a limit of $10g$ for five minutes and $2g$ for 24 hours, with some sort of curve between those two values.
If you're quickly boosting to $.5c$, then coasting for a while, then decelerating at the same rate on the other end, I presume a $27.9ly$ trip would take somewhere on the order of 56 years, and at $.7c$ it would take around 40 years. Is this correct?
I'm aware there are lots of questions and lots of variables here. I think, though, that the problem space is boxed in enough for a creative answer to come out. My apologies if this isn't the case.