When a vet euthanizes a rattie the best method is to use isoflurane gas and then use the shot of euthanasia solution to the heart. The following two articles may help you further:
<https://www.rmca.org/Articles/euthanasia.htm>
<https://web.archive.org/web/20020409145844/http://www.geocities.com/nswfrmc/article7.html>

This is one of the hardest decisions you'll have to make-- it's good to know that you're trying to make it as easy on your rattie as possible.