Yes! There are many good and reliable ways to measure emotions that do not require the use of an FMRI. Below I list some of the ways in which you can assess people's emotions with measures that have been shown to be reliable and valid assessment tools.
Stone, A. A. (1995). Measurement of affective response.
Self-report survey: You could use a self-report survey to measure people's emotions. To get an assessment the emotional responses of your participants, you could administer an emotion-based questionnaire before and after the presentation of a certain stimulus. I didn't see what specific emotions (positive or negative) that you are interested in testing. However, a great scale that I personally have used in my own published research on emotions is the positive and negative affect scale. Here is one of the citations that describes this scale:
Joshanloo, M. (2017). Factor structure and criterion validity of original and short versions of the Negative and Positive Affect Scale (NAPAS). Personality and Individual Differences, 105, 233-237.
Observational measurement: You could also observe the emotional responses of your participants. In this case, you would need to carefully observe (and take copious notes on your observations) of people's reactions to your stimulus to measure their emotional responses. Then you would need to create a coding system to determine the level and severity of their emotional responses. You could also video record your participants and have multiple people rate the emotional reactions of the participants in order to gain a more reliable assessment of those emotional reactions.
Galvanic skin response (GSR): You could also get a physiological measurement that shows the extent to which people are having a stress or emotion-related response to a stimulus. The idea behind this type of measurement is that our skin on our hands will start sweating more when we are having an emotional reaction to a stimulus. So the GSR can help to provide insight to the physiological underpinnings related to the emotional responses of your participants.
Jones, H. E. (1935). The galvanic skin reflex as related to overt emotional expression. The American Journal of Psychology.
Salivary cortisol: Another physiological based approach that is much more feasible than the FMRI is to measure people's salivary cortisol with a cotton swab. Cortisol is a hormone that is released in response to stress. This takes only a short time to administer and is used widely to measure the stress and emotion levels of participants in response to certain stimuli. For example, researchers have shown that people have strong cortisol reactions, as measured by the salivary swabs, when they feel ashamed or embarrassed.
Dickerson, S. S., & Kemeny, M. E. (2004). Acute stressors and cortisol responses: a theoretical integration and synthesis of laboratory research. Psychological bulletin, 130(3), 355.
As you can see, there are many effective ways to measure emotional responses without the use of an FMRI. Indeed, this isn't even an exhaustive list of all the ways you could measure emotions. But I hope that it can help to point you in the direction of thinking of many possible ways that you can assess emotional responses in your research. Good luck!