The document linked below is the one I'm assuming folks are cutting and pasting from:
This document pretty clearly states that you can hunt coyote on a standard hunting license, with no time-of-day restrictions, nor bag limits.
The document also states that "motor vehicles" are not allowed in game areas, and defines "motor vehicles" as "any self-propelled vehicle having at least three wheels and which must be registered as a motor vehicle under Iowa Code Chapter 321."
The document then goes on to define two-way transmitters, and states that coyote hunters may use such devices, but NOT during deer hunting seasons.
The document states that you cannot transport a rifle or shotgun in a motor vehicle on a public highway unless it is broken down, or secured in a case. However, once you leave the "public highway", my guess is as good as yours.
The document also states the restrictions on ATVs, which Boggy listed. You do have to note that ATVs are not the same as "trucks". Also, that section is preceded by the statement:
"“Prohibited acts.” Except as provided, the
use of a motor vehicle on any game management
area by a person without a valid permit, or at any
site not approved on a signed map, is prohibited.
Permits and maps must be carried by the permittee
at all times that the permittee is using a motor
vehicle on a game management area, and must be
exhibited to any DNR employee or law enforcement
official upon request." (p16)
You're not even allowed to DRIVE a truck in a game management area, let alone shoot a weapon out of one. Of course, that restriction is based on the "game management area." Also, the permit referred to in the quote is for folks with movement-based disabilities or physical handicaps. Such a permit only allows the use of the ATV for movement, and doesn't allow said individual to fire a weapon from one.
Laws about firearms discharge are going to cover how and why you can fire a firearm out of a moving vehicle.
As for coyote not being a "game animal"...incorrect. Coyote are classified by the document as both "furbearers" and "small game." You still need a permit to hunt them, and must still abide by the rules for your hunting permit.