Could you give a space telescope an orbit so that it is always in earth's shadow?

Probably not for the simple reason that the earth's shadow does not extend that far into space. The Telescope would have to be orbiting in the same plane as the earth but just a few hundred miles away. That would mean that its orbit would be larger than the earth's and the earth would be orbiting faster than the telescope.

No stay with me on this one.

That means the the telescope would have to orbit faster to keep up with the earth and sty in the exact same orbital position between the earth and the sun. As we are almost already at escape velocity fro the sun's gravitational pull, the telescope might actually have to exceed escape velocity to catch up. That means is would spin off into space.

Good question though.

The L2 point in not in Earth's shadow. The Earth's umbra shadow extends for about 1,400 thousand kilometers. The L2 point is about 100 thousand kilometer further out. So if the space telescope was at L2, the Earth would block a large part of the sun, but not all of it. And besides, it's not practical to stay exactly at the L2 point, you would have to use the control rockets all the time.

The James Webb telescope will orbit around the L2, deliberately to avoid going into the partial shadow. Going in and out of that partial shadow would create stress as the telescope cools down and warms up. Also, using the control thrusters is a stress, and orbiting around the L2 point at a good distance means the thrusters need to be used only once every three weeks.

That would not be in orbit, but stationary. How is the telescope going to remain in space without falling? The L2 Lagrange point is a stable position about 1.5 million km directly opposite the sun, where Earth's shadow is, but it's also at about the point where earth's apparent size matches the sun. I don't know if it would completely block the sun or not.

The James Webb Telescope which will be launched at 2018 is going to orbit the Sun at Earth's L2 Lagrange point which is the opposite side from the Sun.

You couldn't, but... why would you need to? Two solutions: Do what Hubble does - it has a sunshade to eliminate any glare on the primary aperture... or, simply place a shade - maybe a 20-foot diameter piece of mylar between the scope and the sun.