There can be copyright issues.
Even when the copyright holder (the creator of the work or the one to whom any rights were transferred) is hard to locate, this does not mean that the work is then free for anyone to use. This is one of the problems Google ran into in copying "orphaned" works (works with unknown authors). Many of these works
had authors who, in discovering the infringement by Google, came forward saying, "Hey! That's mine."
And Google was sued as a result.
If you did not create it, and if a work is not in the public domain (published prior to 1923)*, then you (generally) must get permission from the copyright holder to use it.
Now, with all of that said, it is
possible in some cases and under some circumstances to use another's copyrighted work as part of your own work. This is called "fair use." Fair use of another's copyrighted work, however, is looked at on a case-by-case basis, by a court, after the use of a copyrighted work has caught the attention of the copyright holder and the copyright holder doesn't much care for the use of his work and sues (or, at least, sends a notice of infringement threatening suit and demanding X amount of dollars to settle).
Appropriation artist Jeffrey Koons has been sued several times for copyright infringement. He has won some suits and lost others. The suits arise because Koons often uses the copyrighted works of others as inspiration for his own work. Ironically, Koons not too long ago sued another artist for appropriating
his works (Balloon Dogs) to create balloon dog bookends. Koons has since dropped the lawsuit.
You can find the text of the Koons copyright infringement lawsuits online. Although there have been several, two you may wish to look at are:
Rogers v Koons, 960 F.2d 301 (2d Cir 1992) - This suit over Koons' use of a photographic image to create a sculpture resulted in a lawsuit loss for Koons, as the court found his use "substantially similar" to the copyrighted image and, therefore, copyright infringement.
Blanche v Koons, No. 03 Civ 8026 (S.D.N.Y. Nov 1, 2005) - Koons used an image taken from an advertisement and used it in his own work. The court found the work transformative and not derivative. Koons won the suit.
The court discussions in the
Koons lawsuits can give you a better idea of how a court looks at using another's copyrighted work as part of your own work, and it can give you a bit of an idea as to how safe your use of a 1950s postcard in your own work could or could not be.
But for the best determination as to whether your work would be infringing on the rights of the postcard artist or not, your specific use would need to be personally reviewed by an attorney in your area. Or, even better, you could continue to look for and then locate the copyright holder, and obtain permission to use the postcard art from the artist. Otherwise, to be legally safe, I suggest it is best that you don't use the postcard art at all.
Good luck.
*Public domain works include more than just works published prior to 1923 - you can go to
http://www.copyright.gov for more information on works in the public domain.