How would you handle difficult customers who don't speak my language?

If you cant communicate then that is a problem easily solved by an interpreter. However, your interpreter needs to be of a similar mind to you and be able to convey the right "vibes". Being confused doesnt help the matters resolution.

looking for one who can speck the same language and handle the customer  instead of you.

Try to learn some key words and phrases in their language.

don't forget to check on their culture also.

Regards

What I would suggest and what I have done in the past on events is I find a person who is passing by who I feel can speak the language and ask him to translate what the disappointed customer is trying to say. For example, I am not an arabic speaker and when someone reaches out to me to complain in arabic I try to call my management so they can help him and if that takes too long I do what I have mentioned above to solve your problem.

There are many languages we don't speak but we all have a smile which speaks them all. Just give your very best and try to find an interpretor who can assist you and if not be the best and understand the customer and nothing is impoissible you can handle it so nicely and at the end you will be so happy to resolve the situation in such great manner, courtesy and skills.

As long as I am dealing with customers then I need to satisfy them.  I will need to get a translator for them to understand what I am saying. I will do anything to convey the message in a good way.