Not a telescope, not at a small budget.
What you have to look at is an astro-mount. On such a mount, you can put a telescope, and on the telescope you can put the camera.
You say you tried simple astrophotography. You should have seen the stars become trails with longer exposures or longer focal lenghts.
That's because of the rotating Earth. If you want to do astrophotography, you need a mount which tracks the stars, against the movement of Earth.
You can buy a telescope for $10.000, but without a mount, no photography.
With simple lenses (also 35mm and telelenses) and a bit more expensive mount, you can do astrophotography.
I got a simple EQ3-2 mount with motors, it costed me $120. Bought a 135mm 2,8 with it, which costed me $15.
Here you can see what I did with it, for the first time I did astrophotography: http://www.cameralabs.com/forum/viewtopic.php?t=24104
I havent uploaded many astronomy pictures, but at least I can let you see this onehttp://www.cameralabs.com/forum/viewtopic.php?t=24536
Only 30s shots with a 200mm lens, with the mount you can get 2 mins with that lens.
So, what do I recommend you to do?
1) Get a mount. Look at the used market as they are new a bit too expensive, maybe. The EQ3-2 mount is the cheapest astrophotography mount, you NEED motors.
2) A remote control is handy, eBay has many at a very low price point. Buy via the ''support us'' page on this site if you want to give Gordon another breakfast
3) If the EQ3-2 doesnt have a polarfinder, you need too one.
4) Look on the internet for objects you can photograph with the lenses you have. The Milkyway galaxy and the Swan region are nice parts of the sky.
5) Download the polarfinder program, which lets you see where exactly the polarfinder is in the sky, for aligning the Earth-as.
6) Shoot in RAW only. Set the ISO almost the highest possible, at 3200.
Set the exposure on 30s, or if you have a remote: BULB.
7) Download the free DeepSkyStacker software, and look for a manual in your language. After stacking, you can edit the final picture too in DSS (DeepSkyS...).
And dont forget to have fun!