I've done this before making elements of a template conditional based on the domain name, and that can work well. I suppose you could extend the same logic to change the template.
Perhaps you could add a conditional to both template's index.php to change the template. Perhaps something like...
if ( substr_count( $_SERVER['HTTP_HOST'], "silly") ) {
$GLOBALS["mainframe"]->setTemplate = "silly_template_name";
} else {
$GLOBALS["mainframe"]->setTemplate = "serious_template_name";
}
...I've not tested this, but I think in principle it should work fine, though it might depend on which Joomla version you have.
There are, as saji89 pointed out, plenty of good multi-site extensions and that'd be an ok solution too.