If you want to choose your own specific colors to go through it here is a quick mod. replace the array colors with either color names or #hexcodes.
Code:
<!--
// ####################################################
// ######## RainBow Text Effect for UserNames #########
// ################# By Neeraj Sinha ##################
// ### Please leave these comments if you are using ###
// ##### http://apnigang.com/forums/index.php #####
// ####################################################
function rain()
{
var aspans = document.getElementsByTagName('span');
for (var i = 0; i < aspans.length; i++)
{
if (aspans[i].className =='rainbow')
{
var words=aspans[i].innerHTML;
var spacer="";
var rainText="";
var colourscheme=new Array("magenta","gold","white","blue","red","green","yellow","orange","gray","purple","pink","lime","cyan","teal","indigo","lightblue")
for(var ch=0;ch<=(words.length-1);ch++){
var c1=Math.round(Math.random()*(colourscheme.length-1));
rainText+="<strong><font color=\""+colourscheme[c1]+"\">"+words[ch]+"</font></strong>";
}
aspans[i].innerHTML=rainText;
}
}
}
// End -->