How can I define my own keyboard combination for sending signals to a script? I'd like to define <Ctrl-blah> to SIGUSR1.

No, but you can change the default key bindings from SIGINT=c-c, SIGQUIT=c-\, SIGTSTP=c-z. (To clarify, you can make c-k send a SIGINT instead of c-c, but you can't use a new signal like SIGUSR1.)

However, you can use the three existing signals for whatever you wish. You can also switch off canon mode, process the keystrokes yourself, and emulate such a behaiviour. All you have to do is to kill 0, SIGUSR1(); when the user presses Ctrl-blah.

Update: I forgot to say this: see info "(libc)Special Characters" for more info, if you have glibc.