Take a look at the OnObjectKeystroke Script trigger. You can set it on a field so that a script is performed with each keystroke. The script can then detetect when enter or return is pressed and perform a script that takes you to the same field, but in the next record. If you are using table view, make sure that the field is present on the layout when you view it in layout mode or you won't be able to set it up with a script trigger.
In Table view: control-down-arrow (ctrl-↓).
If that doesn't work, change the System Preferences:Keyboard:Keyboard Shortcuts:Mission Control to f9 instead of control-down-arrow
Thanks for the info. control-arrow-down does work, but I will try the script thing too. I have yet to try to write a script and last time I looked was a bit intimidated. But it would be good to learn