To date, no one has provided any verifiable answer. However there are a quite a few comments and answers in which the author provides an answer that is very likely wrong due to perception bias. I'm posting this answer mainly to explain how easily perception can lead to mistakes in these conclusions.
TL;DR It's easy to make a mistake when relying on your perception. The only ways to be certain of the accuracy of an answer is if it a) references developer discussion or sample code, or b) applied rigorous testing techniques to create a statistical picture of the drop rates.
The first problem is a question of where your attention is focused. As you place your instant-kill (such as Cherry Bomb or Squash), you are usually looking directly at the place where a number of zombies are killed. Even the Potato Mines make a distinctive sound when they explode drawing your attention. As a result, you'll usually have no trouble noticing any coins that drop. However, if you're busy focusing on gathering sun, and placing more plants on the left hand side of the screen while a zombie is passively killed on right - it's much easier to miss coin drops.
Furthermore, most instant-kills will kill multiple zombies at a time. If there's a flat percentage chance for a zombie to drop a coin when it dies; then multiple zombies dying at the same time will have a higher chance of a coin drop. You then start to form this idea that instant-kills drop more coins.
This leads on to the next problem: you have a (possibly false) perception that more coins drop from instant-kills; so every time you notice it, you think to yourself "aha - there it happened again!". But you forget to take note of the number of times instant-kills didn't drop a coin!
Finally, some people suggested stronger zombies have a higher chance of dropping coins. This is quite possible, but can also be a result of mistaken perception. Remember, the stronger zombies typically come later in a level; along with many more of the weaker zombies. As a result, many more zombies are dying and many more coins are dropping. Similarly, as per the question: when you have a good setup and you're killing zombies efficiently, they're coming much more frequently and in larger waves. You also have more time to notice coin drops because there's no longer a rush to build.
From a programming perspective there are a number of ways the developers could have chosen to vary the drop rates. (Assuming there is any variation at all apart from Yeti zombie.)
It would be very easy for different types of zombies to have different drop rates. This would only need an extra attribute on each zombie to indicate it's percentage drop rate.
A little more work would be needed to have different plants affect drop rate because when plants damage zombies, they would now also need to indicate a type of damage or source of damage. So that when a zombie dies from that damage, the appropriate drop rate rule can be applied.
However, if the developers did do something to affect drop rate of coins, I would have expected them to leave some sort of clue to that effect. Either in the Almanac or from the Tree of Wisdom.
Finally I did conduct a little experiment myself:
I played only one level of survival. First game limiting myself only to explosive plants. Second game limiting myself only to Pea Shooters. In both games, exactly the same number of coins dropped.
Please note, this sample size is far too small to draw any meaningful conclusion and obviously I only encountered low level zombies). Unfortunately I don't have the time to experiment more thoroughly. But if someone else has the inclination it would be interesting to see the results. (To determine if type of zombie affects drop rate, you would probably have to record your games to get a reliable count of the number of zombies of each type.)