The International Space Station has a Ham Radio station, and I've heard that the station frequently makes contact with people on the ground. I've seen the crew timelines, but they only publish what happened in the past.
There is an international organisation of amateur radio societies from the ISS partner countries with a volunteer working group devoted to developing and putting into operation the ISS amateur radio station, and they go by the name ARISS (Amateur Radio on the International Space Station).
The ARISS program is a cooperative venture of NASA, the ARRL and AMSAT and other international space agencies that organizes scheduled contacts via Amateur Radio between astronauts and cosmonauts aboard the ISS and classrooms and communities. With the help of experienced Amateur Radio volunteers from Amateur Radio clubs, and coordination from the ARISS Team, the ISS crewmembers speak directly with large group audiences in a variety of public forums such as school assemblies or at science museums, Scout camporees and jamborees and space camps, where students, teachers, parents, and communities learn about space and space technologies and Amateur Radio.
About pre-published timetables however, and according to NASA page on ARISS:
ARISS contacts are typically not a good fit for events that take place on a specific date. ARISS contacts are subject to real-time mission operations and often move around on the schedule. Host organizations must be flexible and prepared to reschedule their ARISS event.
But there are occasional announcements of scheduled amateur radio contacts with the ISS, either on ARISS international, on the individual nations' ARISS pages, or other pages of other associated members. Not in any particular order, some of these are:
- Belgium: AMSAT-Belgium and UBA
- Portugal: AMSAT-CT and REP
- Italy: AMSAT-Italy and ARI
- Sweden: AMSAT-SM
- United Kingdom: AMSAT-UK and RSGB
- Germany: DARC
- Malta: MARL
- Poland: PZK
- Lebanon: RAL
- France: REF-Union
- Switzerland: USKA
- The Netherlands: VERON
- Japan: JARL
For example, following these pages around a bit more, I was able to find a link to a published RTF document on Upcoming ARISS Contact Schedule (as of 2013-08-30 22:00 UTC) that is still somewhat current as of the time and date of this answer:
Quick list of scheduled contacts and events:
Amicale Space Camp organized by Sterrenlab for children of the European Patent Office/NL, Leiden, The Netherlands (Summer Space Camp, Noordwijk, Netherlands), Netherlands, via PA3GUO Contact was successful: Fri 2013-08-30 12:11:43 UTC 55 deg
Gwalior Glory High School, Gwalior, Madhya Pradesh, India, telebridge via IK1SLD Contact is a go for: Sat 2013-08-31 11:22:58 UTC 43 deg
Mill Springs Academy, Alpharetta, GA, direct via KK4OVR Contact is a go for: Wed 2013-09-04 14:15:45 UTC 40 deg
Duluth Children's Museum, Duluth, MN, direct via WØGKP Contact is a go for: Sat 2013-09-07 15:03:34 UTC 67 deg
ARISS is requesting listener reports for the above contacts. Due to issues with the Kenwood radio that are not fully understood at present, the Ericsson radio is going to be used for these contacts. ARISS thanks everyone in advance for their assistance.
More information and a lot of useful links are in the mentioned document and on the American Radio Relay League (ARRL) page on Amateur Radio on the International Space Station.
So in short, following ARISS contacts and pre-announced radio contact schedules with the ISS is a bit tricky for non-member of any of these organisations listed, but still possible. I imagine schools that are members of any of these amateur radio organisations receive notifications also through newsletters they're subscribed to, or other channels.
I really, really hate saying this, but I'm afraid not.
My reasoning? I, and probably many others, have been Googling like crazy to find the answer to this for three weeks. If there were a pre-published time, then one would think that it would come up as one of the first results for a search like
iss ham radio contact or
iss ham radio time.
I'm very eager to be proven wrong, but it certainly seems that this information wouldn't be hidden deep in the 35th page of Google.
It seems like the best thing that can be done for this is to look at the times they have in the past, and try to be on at the same time. Bottom line, you just have to keep trying, and hopefully some day you'll get lucky. But they don't publish schedules ahead of time, just after the fact.