You can't pause it like the non-colored tamagotchi. What I do is go to the time, leave at the set mode, so it will be "paused". If you are going away for a long time, I would suggest that you take out the batteries. But do remember to click resume after you load the batteries in.
Well, with the P's you actually have a couple of options, If you have a toddler/teen character you can drop them off at the daycare. I think that is available from 10am-3pm? Once you have an older character you can leave them at school or work. I use these options while I am away at work. I haven't had any issues yet. Although, keep in mind that the hunger and happy meters will not stay full as they do when you pause a different version. You will need to periodically check in if you are worried about care misses