If the number of your messages is limited then the following may help. I used jQuery for the following example, but it works with plain js too.
The innerHtml property did not work for me. So I experimented with ...
<div id=successAndErrorMessages-1>100% OK</div>
<div id=successAndErrorMessages-2>This is an error mssg!</div>
and toggled one of the two on/off ...
$("#successAndErrorMessages-1").css('display', 'none')
$("#successAndErrorMessages-2").css('display', '')
For some reason I had to fiddle around with the ordering before it worked in all types of browsers.