Senza le regular expressions, parti da qui:
codice:
var myString= "ababababa";
var mySubString= "aba";
var count = 0;
for (var i = 0; i <= myString.length - mySubString.length; i++)
{
    if (myString.substring(i, i + mySubString.length) == mySubString)
    {
        count++;
    }
}

alert(count);
HTH
Zappa