If you want to give specific users their own colour, then you can do so by pressing Alt + B. Go into the NICK section and assign different colours to people either by nickname or mask (e.g.: LadyDana or *!dana@*.fluffyclouds.org).

If you want to randomize colours, then you can try the following remote snippet:
Code:
On *:JOIN:#:{
  if ($nick == $me) {
    var %i = 1, %c = 1
    while (%i <= $nick(#,0)) {
      if (%c > 15) { set %c 1 }
      if (%c == $color(background color)) { inc %c }
      cline %c # %i
      inc %i
      inc %c
    }
  }
}

... or something along those lines. I can't verify everything sorry, don't have a copy of mIRC handy.

Dana