In your Google Calendar (if you keep one already, you can use it; if you don't, you can make one just for conferences), you can set a region of time up as 30-minute appointment slots. Then when those slips of paper come back in, you can just click on a slot and enter the name.
If you want more automation, you can send the URL out to parents and they can sign up from home... no more slips of paper! Unfortunately, this only works for parents who have a Google Username (gmail, google docs, etc.).
Here is a video tutorial about using appointment slots in Google Calendar: