First officer of undisclosed aircraft type reports localizer fluctuations on the LDA DME Runway 19 to DCA.

Narrative

I have been into DCA twice in the past month and each time we were told to fly the LDA DME Runway 19 approach. This approach brings you in over the river much like the visual approach would have you do; and luckily both days I had to shoot this approach the weather favored visual conditions. My concern with the approach is that the localizer is very erratic. The localizer needle will swing from right to left and vice versa. I have never seen the needle actually stabilized. Both times we hand flew the approach since the autopilot was very confused and made unnecessary turns. We didn't want to risk getting into P56. The last time I was on the approach; I kept a close watch of our ground track in relation to what it shows on the approach plate; and the needle proceeded to swing from right to left and remain unstable. For a place that allows so little error; I think we should be able to depend on an approach that is a little more reliable. A lot of crews I think would be very close to not only busting through P56; but also a very unstable descent and tracking if they would have to perform in complete IMC.