Unless the children are very similar in standard and stay similar in standard, I'd say you'd be better booking an hour every 4 weeks for an individual lesson and hiring a public court for yourself for the other three weeks and doing practice yourself.
Book a coach and share him/her between your child and one or three others for the hour. This way you get a manageable group of children you know, the time split up nicely by the coach and halve or quarter the price. A group of four kids who know each other is pretty manageable and they will all learn a lot.
Maybe I should take up coaching again <joins Moomin in a faint>
If you can hit a ball and throw reasonably accurately, then you can do it for the time being.
Also if you can find a blank wall he can hit against, that does a lot for learning. I spent a lot of time hitting a ball against the wall. You have to learn exactly how hard to hit, as the ball comes back! I only had a space of wall about 3m long and 2m high, and a driveway width to play on, but I spent hours doing that. You learn accuracy and timing from that.
I've done some tennis coaching back ages ago. The group lessons in the main part aren't worth much. Basically they get some time on court with a ball and raquet-you can do as much yourself. £45 is steep though, it was about £15 when I was having lessons about 20 year ago, and you didn't have to be a member of the club either. Try looking for some smaller clubs, or even public courts sometimes have coaches that use them.
Get an ordinary bucket. Fill it with decent tennis balls (if they're loose then drop them and see how well they bounce) you shouldn't be able to compress them much by squeezing. Take him to the court, and throw balls at him. With my dc I usually start with 1 bucket of forehands, 1 of backhands. Then you can do more fun formations if he's ready for varieties. You can do alternate forehand/backhands, or randomly. Do groups, so he starts far right hand corner and does a set of 4 moving closer to the net each ball, ending up with a volley. Or you can do one base line shot, run straight to the net forehand volley, backhand volley, smash... type of groupings.
Or go down to a club, watch and find someone who looks reasonable and ask if they coach. My first coach took me for an hour lesson in return for a mars bar. He just loved coaching, and was at least as good as any professional coach, although more unorthodox .