The Colornote support page gives a few options. You can sync through their online services, by transferable backup, or by SD card.
How to transfer notes from old phone to new phone.
Using the online sync is Recommended.
Sign up online sync on your old phone. Go to:
Menu –-> Backup –-> Sign Up.
next Sync your device by going to:
Menu –-> Sync. Check how many notes are synced by going to: Menu -–> Settings –-> Online Backup –-> Synced notes.
Then sign in to online sync in your new phone by going to:
Menu –-> Backup -–> Sign In.
Using sdcard backup:
the steps below to transfer notes saved on the previous device to the new device using local backup.
When you have the previous device
Open ColorNote and go to the device backup screen on the previous device go to:
Menu --> Backup --> Tap Device
Which is located in the upper bar or go to:
Settings --> Backup.
Next manually back up notes by pressing:
Backup Notes --> Enter master password --> Done.
then move the backed up files from the previous device to the new device.
Go to sdcard backup screen on your old phone by:
Menu –-> Backup -–> SD card backup.
To Backup Notes you need to press the button and then enter your master password.
Lastly, move sdcard from old phone to new phone.
Go to sdcard backup screen on your new phone and tap backup item you want to restore.
finish up by typing the password that you have set when backup file was created.