What should I do if I have an idea but can't work on it immediately?
Now you are a postdoc and not a graduate student anymore. As such, you will have many research ideas, that you will not have the time to implement yourself. So, it is time for you to start delegating this work to "less experienced" workforce than you. That means undergraduate, master or PHD students. So, you should discuss it with your advisor that you have a new idea and that you are planning to propose a new undergraduate or MSc thesis. Perhaps he might even propose, working with a graduate student who is a bit stuck at his current stage of his / her PHD, so working in your new idea might be beneficial to both of you.

In any of these cases, co-authorship issues should be discussed early and thorough. For undergraduate, MSc students usually the assumption is that they do most of the work (it is their thesis after all) but you write the paper and you get to be first author. For teaming with PHD students, things are a little bit trickier, so these issues should be discussed in detail, BEFORE the cooperation begins. Also, make sure that your PI is OK not to be included in the subsequent publication (since this is your idea after all). Of course, if you want to include your PI in your "additional" publication then by all means, go ahead (this will also help you bend his objections about the time you will spend on your new project). But if you do not, make sure you discuss it before doing it, so you will not get into hot water.

In this scheme, not only you can multiply the number of your publications more easily and faster but also you help other people, who might be your future collaborators. So, you really have nothing to lose.