Photographs of outdoor scenes or of urban areas provide a neutral background, while lending the set an authentic look. Stores offering photographic services will blow up and print the photo to the specific size that you need. If you're making the prop for a school play, maybe you'd want to use a picture of the animal that serves as your school mascot.
Pick out a logo of a favorite TV show or movie and paint it as the background for the television prop. Maybe you had a cast and crew party where you all watched a certain movie or show together that you could use.
Many productions will take official group photos of the cast and crew. Consider blowing one up for use as the background of the TV prop.
When people work so closely together, as they do during the production of a play, cast and crew members often develop inside jokes. Think of a picture that best represents one potential joke and use it as the TV background. It may leave audience members scratching their heads, but it serves as a great reminder to those in the play of the fun times you all had.
A diorama can give the TV a 3-D appearance. While unconventional, if you have a lot of time on your hands to build the set, create a diorama within the television prop. This is especially something to consider if it's a science fiction or fantasy play, where reality is different from the one we know.
One funny or eerie way to introduce a TV prop into the background is to paint a television screen that is displaying static. It hints at a reality that is at least partially compromised.
Many plays take place in times other than the present. If the play for which you are building a set takes place before 1954, when color television broadcasting debuted, make the background some type of black-and-white picture for historical accuracy.
Think up your own show or one mentioned in the play, and use the logo from it in the background for the TV. If you're using a TV show you made up, you'll need to take the extra step and make up a logo too. This is a perfect chance to let your creativity shine through.