You are designing the creature, so yes
There is a skeptics SE question on this subject, relating to humans. This seems to support the claim that mental state can have some difference on an eye colour - mostly through anecdotal 'evidence' though. It doesn't necessarily mean human eyes can have rapid drastic changes though (blue to red instantly, for example, would require a very fast change in the amount of melanin and may not be healthy).
You could, however, have a different structure to your creatures entirely. Perhaps the chemicals that drive emotions, once in the blood stream, refract light differently and make the colours. Perhaps your creatures have various protective filters on their eyes - under stress a creature on a desert planet may have an automatic dust filter which comes down and this scatters or reflects red light more - making the eyes appear red.
There are many methods you could apply. Your question only asks for if they could, not how they would though so I won't go into that too much here.
Edit to add the how:
There are lots of ways to do this:
* Moisture traps: This idea comes from the Charidotella egregia which traps water between different layers of thin reflective surfaces as described in this paper (even if only the abstract is available it describes this process fairly simply). The moisture changes the distance between these reflective films and, by varying the amount of moisture, the distance between reflective films can be controlled.
* I like this method because it gives fine control over colour change and can be related to something more human - crying. Interestingly we have different types of tears I would imagine the salinity of your creatures tears could effect how easily the porous layers of film absorb and, therefore, produce different colours.
* This is a very fast acting method.
* This also requires little effort (no producing complicated dyes or such that this may be an evolutionary disadvantage).
* Colour cells: Cuttlefish are, I've been finding out, rather amazing colour changers. 762
Here is a quote from that article:
Cuttlefish skin has been likened to a color television—it has a way of combining basic colors to form more complex hues and dynamic patterns. "It really is electric skin," <PERSON> said, because it's all controlled by neurons in the brain that transmit impulses and information to the rest of the body. "A cuttlefish has maybe ten million little color cells in its skin, and each one of them is controlled by a neuron. If you turn some on, but leave others switched off, you can create patterns," <PERSON> explained.
* This method is brilliant colour control, fast acting and we can link it into the brain fairly easily since it is controlled by electrical impulses. It would require having these colour cells in the iris (perhaps as a method to better see in different lights). These could be related to emotion in many different ways but a few that occurred to me:
* When sad humans often look down where we receive fewer distractions as we look inside ourselves. This could be substituted by a darker pigment blocking out more light.
* Anger in humans can cause dilated pupils, perhaps to take in more light. In our creatures they could do this by changing to lighter irises, revealing the crisscross of blood-vessels behind the eye and creating a red eye look (as with albinos).
Those last couple of points could apply to either technique or any of those other answers have mentioned. 762