Short answer: It is theoretically possible, but I am not aware of any tools that will let you create custom videos to play on your particular digital camera. So practically, no.
You said you tried to convert your computer videos to MOV files and copied them to your SD card. However, this procedure is by far not enough. MOV is a very general video container format, and there are many choices of codecs and sub-choices within a codec. For example (this is not authoritative), maybe your camera only supports MOV files encoded with the AVC/H.264 video codec baseline profile with a keyframe every 30 frames, and uncompressed 16-bit PCM stereo audio at 48 kHz. Also, maybe your camera demands the MOV file to have certain custom information tags, maximum frame size limits, audio/video interleaving constraints, and literally dozens of other subtle constraints.
So, if you can produce a MOV file that meets all those (usually unstated) constraints, then your digital camera will be able to play it back.
Remember, the situation is totally asymmetric here. Your digital camera probably produces MOV video files under a very limited set of codecs and options, and plays back videos encoded under those limited options. By contrast, your computer can play a wide range of MOV files, with different codecs and larger RAM buffers, etc. Just because a MOV file can play on your super-flexible computer does not mean the same file can play on your super-restrictive camera.
Side note: It is often possible inject custom pictures onto a flash memory card to play back on a digital camera. I have demonstrated this successfully on a number of different cameras. The trick that I used was that I saved the custom picture as a basic JPEG image (without progressive encoding, without arithmetic coding) and ensured the width and height were multiples of 8.
