For example:
When typing παιχνιδια.com into Firefox, it is automatically converted to xn--kxadblxczv9d.com
Please suggest a tool for making such a conversion.
One of the easiest is this. Converts and checks for availability at the same time.
You can use any tool that supports "Libidn". A quick search showed SimpleDNS might be of help to you.
There are heaps of converters for IDN online, if that's enough for you, you can use one of them.