The longest timelapse of a Martian moon I'm aware of is this 27 minute long timelapse of Phobos rising at June 28, 2013.
The light conditions, and the relatively small size of Phobos in the sky, makes the effect hard to see.
Phobos goes from horizon to horizon in approximately 4 hours 15 minutes, so this timelapse should cover about a ninth of the path.
At zenith, Phobos is 1.76 Mars radii away, and when setting, 2.57 radii away, and as such, Phobos should appear to have a 46% larger diameter. (only 3.6% for Deimos, which is also even smaller in the night sky).
Unfortunately, the video is centred straight up, so it covers a segment where Phobos both grows larger and shrinks again. With a rough back-of-the-envelope calculation I estimate that as only a 1% change in diameter, so count your pixels!
A video covering Phobos near the horizon would give better results, even if it's shorter.
Here's such a clip from Spirit, but the image quality isn't good enough to see much beyond a moving blurry dot. One would probably need Curiosity footage for this.
Update: here's timelapse of Phobos rising over the horizon, and even slightly longer (32 minutes).
The atmosphere makes it hard to judge size,
That's more like a 13% change, so a much better view.
If there are better timelapses, they are almost certain to be of Phobos, since the greater distance to Deimos makes the effect both weaker and less easy to observe:
(relative size in the sky)