This is a common question.
Sadly there is no international register of these vaccines.
If you DO remember who gave it to you, you can ask them for a new copy. Yellow fever providers are supposed to keep records. ( At Dr Deb's we have some records going back over 30 years )
If you cannot find who gave it to you, you will need to have the vaccine again if you want a new certificate. It is SAFE to have another dose of vaccine. Travellers used to have them every 10 years and in my experience some people lose them frequently and some travellers have had quite a few extra ones over the years. In fact, your risk of side effects from the vaccine is LESS with every subsequent dose.
In Australia you can ask to have the Yellow Fever vaccine entered onto the Australian Immunisation Register.
Now that Yellow Fever vaccine is valid for life, it is even more important that you keep the booklet safe.