Well, usually for AZ mounts and EQ mounts(without motor drives), there's slow motion knobs to recenter the celestial object you're currently looking right? Well, we can take that to an advantage.

How to do astrophotography with telescopes on these mounts? Simple, if it is possible. First slot in the BinoViewer. then slot one of the highpowered eyepiece(The eyepiece power must be similar to the DSLR Camera/CCD Camera) in one, then adapt the Camera into another. So, center the photographic object first, then click the button for the Camera to begin exposure time. If let's say you're taking Jupiter at 156x, the exposure time takes 75 seconds, time you stopwatch at 75 secs or wait for the 75 secs, but meanwhile, look through the eyepiece, then, carry on recentering Jupiter till the exposure's finished with the slow-motion knobs.

I don't know astrophotography that well, so I don't know whether this can work that well, so please forgive if this is somewhat impossible to perform.