I am replying to this post as I do specialise in exactly that area - fun english games for children aged 4-12.
Many teachers rely on photocopiable resources, but I believe that many teachers rely too much on worksheets that takes the students two minutes to fill in.
Have you given any thought to incorporating games into your lessons?
While you might think that it may be hard playing a game with just one student there are a number of things that you can do, such give a limited time for the task using a stopwatch or timer. The student must complete the task before the timer goes off so you add excitement by having a race against the clock. You can also time your student and then see if they can beat their time in the next round.
You can also play too and again there are things you can do to make it a genuine game, rather than one where you either win all the time or pretend to be slow. For example you can give your pupil a head start or make your task harder.
You can find out more about teaching children with games through the site below.
I wish you all the best with your one to one teaching. It's highly rewarding and a valuable skill because you can use the same games and techniques to teach your own children or family members a second language.
Here's a page on
How to teach a child to speak English for face to face lessons.
And this book is for you if you are teaching online:
ESL Online Games - it does one to one, groups and virtual classes.