Yes, both the Canon T1i and the T2i have high-speed continuous shooting. (actually,
all dSLRs have high-speed continuous shooting)
The Canon T1i can shoot as fast as 3.4 frames-per-second (fps). The Canon T2i can do 3.7 fps, although I'm not sure if that 0.3 fps difference is noticeably different.
For high-speed continuous shooting, you'll need to
specifically set the camera to the
Continuous Shooting mode. With Continuous Shooting mode, you can hold the shutter button down, and the camera will take continuous photos at 3.4 - 3.7 fps.
Without Continuous Shooting mode, holding the shutter button down will only take 1 photo.
I'm not sure what you mean by "delay time", since there are several different things you could potentially mean. The
shutter lag time (the time between you pressing the button and the camera actually taking the picture) is 0.089 to 0.159 sec, depending on whether you pre-focus the camera or not.
The
shot-to-shot time (the best possible time between shots) is 0.40 sec, if you're not in Continuous Shooting mode.
The above numbers are for the Canon T1i. Of course, if these times are too slow, you can consider either the Canon 50D or the Canon 7D for faster "delay times".
Hope that helps.