[html] Make div (height) occupy parent remaining height

Unless I am misunderstanding, you can just add height: 100%; and overflow:hidden; to #down.

#down { 
    background:pink; 
    height:100%; 
    overflow:hidden;
}?

Live DEMO

Edit: Since you do not want to use overflow:hidden;, you can use display: table; for this scenario; however, it is not supported prior to IE 8. (display: table; support)

#container { 
    width: 300px; 
    height: 300px; 
    border:1px solid red;
    display:table;
}

#up { 
    background: green;
    display:table-row;
    height:0; 
}

#down { 
    background:pink;
    display:table-row;
}?

Live DEMO

Note: You have said that you want the #down height to be #container height minus #up height. The display:table; solution does exactly that and this jsfiddle will portray that pretty clearly.

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