Your digital frame displat sone number of pixel wide and so many high. So what you need to do is record a two step action. Once you have this action you can batch the action to create a set of images for your digital frame using the image processor script.
Step 1 Menu File>Automate>Fit Image... In the Fit Image Dialog enter your digital frame width and height pixels numbers. The Fit Image Plug-in will record those into the action step. When the action is used no dialog will be displayed the recorded values will be used. Fit Image will resize any size image to fit on your digital frame. The images will retain their Aspect Ratio. Images that have the same Aspect Ratio as your digital frame will fill the frame. Images with different aspect ration will have borders on two sides. Left and Right or Top and Bottom.
Step 2 Menu Image>Canvas Size in the Canvas side Dialog Set your digital frame width and height pixels numbers. Make sure Relative is not checked leave the anchor point centered. Set Black as the addled canvas color. All Image will be the exact size as you digital frame display.
Batch the action use menu File>Scripts>Image Processor... Include the action in its dialog and do not have the script do any resize. The action will resize the images and add any canvas needed.