You could coerce an existing general purpose tool like wget to do this. Although it might take some practice to get the
settings right.
If you have some programming experience and would like to pursue a custom solution then I would recommend Ruby +
Nokogiri or Python + Beautiful Soup. They are libraries specifically designed for this kind of thing. You can also hack
together something manually with regular expressions if you really want to, I used to do that with Perl.
A word of caution. Web site administrators don't usually like it when you do this, especially if you don't
leave pauses in between requests or do something stupid like open 50 concurrent connections at a time. This means you
may (probably) get banned from the site in question (This is how I got banned from Sankaku Complex when I was a student
T_T). Consider taking steps to hide your identity and/or start off with sites you don't mind being banned from.
Since Minitokyo does not even have an auto-refreshing shoutbox, I think it is very unlikely you will get the approval of
the site administrator to do this.