DSN time is competitive, and not cheap.
So, besides the costs that Tom mentioned in getting the camera there (and an appropriate relay satellite), you have to consider the costs of getting the data back to the earth.
For the space station, it's only ~370km (230 miles) up ... relatively close, and they can use much smaller dishes than what's required to get decent telemetry from spacecraft at Mars or even the moon (359 Mm to 406 Mm).
Let's take as an example, the STEREO mission -- each spacecraft gets one or two DSN passes per day, but they're also tracked by smaller dishes in the U.S., Asia, and Europe to try to get near-real-time space weather information. (it was as small as 5.5m dishes early in the mission vs. the 34m and 70m ones from the DSN; they're now using a mix of dishes; I know Bochum is 20m )
Right now, the spacecraft get 480 kbps from the DSN (to decrease to 160kbps when they're near 2AU (300 Gm) from earth). The beacon mode data, as it needs to be downlinked on the smaller dishes ... is closer to 600bps. (sorry, couldn't find a comprehensive telemetry rate table)
In the current plans, under 2013 week 37, they expect 'Significant telemetry shortfalls'. That's the competitive nature -- it might be that some other spacecraft with a higher priority is in the same region of the sky. (eg, we get less time when one of the spacecraft is in the same direction from earth as mars, or when there's a major launch)
We get donated time for STEREO beacon because the data's of value to many groups ... I'm not sure that you'd be able to get the same for something that's just for public outreach. (Crowd funding might work, but if the images are really boring, maybe not)
Disclaimer : I work for the Solar Data Analysis Center, which oversees the STEREO beacon data processing.