Preferably Firefox would be used. If the site says incorrect browser with Firefox, you could try installing the User Agent Switcher extension (
https://addons.mozilla.org/en-US/firefox/addon/59). After installation, click Tools->User Agent Switcher->Internet Explorer 7. When you are done using the site, change this back to Default.
However, if that does not work, you could try using Internet Explorer under Parallels ($80,
http://www.parallels.com/en/desktop/), VMware Fusion ($80,
http://www.vmware.com/products/fusion/), or VirtualBox (free,
http://www.virtualbox.org). These are both virtualization products; a Windows license and installer CD/DVD (expensive) are required in addition to the cost of the virtualization program.
A cheaper option would be to use CrossOver ($40,
http://www.codeweavers.com/products/cxmac) which has an easy installer for Internet Explorer and works with many other Windows apps without requiring a Windows license.
If you really do not want to pay at all, you could use Darwine (free,
http://www.kronenberg.org/darwine/) or a MacPorts version of WINE (free,
http://www.macports.org) and run the Internet Explorer installer there, although this sometimes is error-prone and confusing.