Get your kids to play some blitz chess, and correct him everytime he forget, so that he get used to it. Maby you could give them some reward (candy or something) if they play a whole blitz game without forgetting.
How tcan a child learn to press the clock

Play some blitz or rapid chess with him. Never move unless he hits the clock. The more thoughtful you can look while you're using his time to ponder the position, or calculate pi in your head, or inspecting your fingernails, the better.
That would be much better than correcting him all the time. The only thing he's going to get used to is that his opponent will be kind enough to remind him when he's forgot the clock - that is not a good lesson to learn. Also, getting corrected all the time is annoying. Kids tend to go on strike when they're getting annoyed.
I wouldn't hand out candy rewards for any of this. If he likes to play chess and wants to get better, he will realize soon enough it's in his favor to learn to press the clock.

Right, this is also my observation. My son became very raging when I corrected him on every move. May be I should play a Blitz with him, 1 minute for me and 5 for him. But currently he hate Blitzchess because he hate the clock.
He is a "high sensible" kid and one characteristic trait of this type of children is that they have an objection against time pressure.
Thomas

Rap him sharply over the knuckles with a toffee hammer every time he forgets. If he gets uppity about this "medicine", send him to his room with no supper. It's the only way he'll learn.

What I recently started playing with a friend (25 years) who I've taught chess to only recently is 1 hour vs. 5 min chess. One hour sounds like a lot of time, so it should make him more willing to play, and still leaves you with the opportunity to look thoughtful without moving when he forgets to press the clock.
It might be a better option if he hates blitz and likes thinking, which is something to be encouraged.
Also, teach his sister to kick his ass. My sister is two years younger and is still about my equal, but she was loads better than me for a time. It grabs one's pride and helps one improve.

The suggestions outlined above are good: he'll eventually start pressing the clock, if you sit there and "ponder". I began playing chess in my mid-teens and would like to think I have a good attention span, yet it took me a while to get used to hitting the clock as well. Practice makes perfect, and he'll master it eventually.
However, if he hates blitz, don't push him to play blitz. Chess should be fun.
Hi,
my two kids, 6 years and 8 years, play chess.
My daugther has no problem with the chess clock. She internalized to press the clock when she did a move.
However my son, two years older, already played more tournaments than my daugther but he still have problems to remember to press the clock.
This is not a real problem in "long games" because kids have usually enough time for their games but is critical in short games.
Is there a good training method that enables kids to play with the chess clock?
Thomas