A simple antenna has at least one dimension that is approximately, or larger than,
$$L = \frac{1}{4} \lambda = \frac{1}{4} \frac{c}{f}$$
where $\lambda$ is the wavelength, which can be computed from the speed of light $c$ and the frequency $f$. For 137 MHz, that's 55 cm or 1.8 ft. That's a pretty big PCB! At 1090 MHz, this is less of a problem, though.
The next question is what design you're using. The simplest antenna design is a rigid wire one quarter wavelength long (the length I mentioned above), but if that is what you want, a piece of solid-core wire is cheaper and easier to obtain than a PCB.
Some more complex antennas that can be readily made on PCBs are specifically wide-bandwidth, for receiving over an unusually wide frequency range, or more directional, for long-range point to point communication — both not being the problem these applications are trying to solve.
And the squiggly complicated PCB antennas you may have seen are trying to solve the problem of stuffing a decent antenna, with needed electrical properties, into a tiny space, as in a cell phone. (Or just avoiding needing a separate component to solder on.) The tradeoff is that these ‘electrically small’ antennas may have different matching requirements, narrower bandwidth, and be less efficient, which matters mostly for transmission.
So, overall, yes, you could make a PCB antenna for these signals, but it's not the right technology.