How about sandcasters? Originally a defensive weapons system from Traveller, the original concept was a low velocity weapon throwing out a canister of common sand. A bursting charge destroyed the canister and dispersed the sand. In that system, it was to defend against lasers, but when you consider the velocities that are being discussed here, it would work fairly well against any high velocity system.
At sufficient speeds, running into sand particles is just like running into a brick wall.
For that matter, if you had a good aggregate of powder sand up to small stones, it would work pretty well against any of the weapon systems discussed. You would still have stuff penetrating, but their would be an effect. Small stones in the path of a missile running 30,000 km/s is going to play hell with that missile.
Dispersion from the bursting charge is going to eventually spread the screen out, and the velocity of the firing ship is going to carry it past the screen rapidly. BUT if you dropped them along the bearing of the enemy firing at you, where you GOING to be, they could be fairly effective.
I've thought about similar things, both for this application, and for destroying laser mirrors. The laser mirror application turned out to be quite practical, but I'll have to do the math on the anti-kinetic use.
As to the viability of railguns, both sides are correct. If the projectile could be accelerated entirely uniformly, then it would be possible for the projectile to undergo arbitrary accelerations. However, something like the Roche Limit (which only applies to orbital bodies, due to tidal forces) will apply if "tidal forces" are present for whatever reason, either due to non-uniform force application, or due to non-uniform fields. I'm not sure how assumptions like uniform charge distribution will hold up in these cases. It could be that the electrons are physically ripped out of the material. I also think that non-uniform fields will be a problem. Normally, one can assume that, for example, the field inside a solenoid is uniform, but I'm not sure about it in this case.
The above comments can be taken about any for of kinetic launcher, be it railgun, coilgun, gravdriver, ram cannon, or what have you.
As for the specific case of railguns, I'm really skeptical. They generally rely on physical contact with the rails, and good luck with that at 100 km/s.
And please, no force fields. I do like the doppler radar idea, though.
Edit:
I've done some very rough math on the sandcaster thing. I could be entirely out to lunch on how I went about it, but it should at least be a starting point.
Assume a grain of sand (Silica) impacts a tungsten projectile at 200 km/s. The grain has a diameter of .5 mm, and a mass of 1.73e-7 kg.
It should produce a total impulse of about 24 N*s, and a force of about 57 MN.
Please take these numbers with a very large grain of salt. However, I do believe that they should be indicative of the order of magnitude that we're dealing with.
My conclusion is that it while a grain this size should be able to shatter or deflect the target projectile, I'm not sure if it is possible to achieve the required particle density. To cover an area against a projectile that has a diameter of 2 cm will take 3183 particles/m^2 (assuming perfect distribution) and will take about .55 grams/m^2. However, I'm not sure you could accurately disperse that many particles, and then, how do you get them to stop dispersing?
Also, remember that the fragments of the projectile in question are still out there, and heading for your ship. The main advantage to this is that the projectile is neither a long rod, nor guided anymore.