PUT to update the specified order...

/api/v2/orders/:id
/api/v2/orders/:id/update
/api/v2/orders/:id/update.xml

For example...

<?xml version="1.0" encoding="UTF-8"?>
<order>
    <id>1</id>
    <first_name>Bugs</first_name>
    <last_name>Bunny</last_name>
    <email>bugs@bunny.com</email>
    <currency>USD</currency>
    <custom_1>Optional</custom_1>
    <custom_2>Custom</custom_2>
    <custom_3>Values</custom_3>
    <expiration_date type="datetime">2010-09-07T15:08:02+00:00</expiration_date>
    <download_limit type="integer">5</download_limit>
    <send_email>false</send_email>
    <order_items type="array">
        <order_item>
            <sku>1</sku>
            <downloads_remaining type="integer">4</downloads_remaining>
            <price type="float">4.99</price>
        </order_item>
    </order_items>
</order>

NOTE: price is optional and defaults to the price set in the UI if not present.send_email is optional and defaults to false if not present. All fields can be changed including the order ID.