How can I do continous shooting at 10 second intervals on my CoolPix p900?

According to the Nikon Coolpix D900 user manual, there are only 2 ways to capture a timelapse with the Coolpix P900 : using the Timelapse Movie capture or the Interval Timer.

Timelapse Movie

The P900 can shoot small video clips of 10s in 1080p by taking up to 300 pictures at different intervals (between 2s and 36s). See user manual page 97 for operation details. This can come handy for sharing the timelapse in video format for immediate viewing. However, the captured images are set in stone. It is difficult to retouch them in post production with photo tools as you'll need to extract each frame as jpeg. Also, jpeg is a pretty limiting format for retouching.

Interval Timer

you can use the Interval Timer (Page 153). This method allows to take full quality pictures at programmed intervals. The User Manual does state anything about the minimum interval value.

If what you say is correct, intervals cannot be set below 30s. I would first check for firmware update. I think there's little hope that it would fix it, but we never know.

As opposed to DSLR, this camera does not allow the use of an external intervalometer that could bypass the camera limitations. Moreover, the mobile app that pairs with the P900 (i.e. Wireless Mobile Utility) forbid the use of the Interval Timer in Continuous.

All in all, if you want 10s intervals for your timelapse shot, you will have to use the Timelapse Movie capture option and work it all in-camera (white balance, color, contrast...) and take into account camera limitations. If you happen to do that very often, maybe it's time to upgrade to DSLR...

DIY Nikon IR Intervalometer. Just change the delay in the code from 60 to 10.