Could you elaborate on your understandning of meta-emotion?
One option for assessing emotions indirectly would be to use non-obstrusive measures of autonimic responses e.g. skin conductance of heart rate, which works pretty well in children, too.
Meta-emotion is "an organized and structured set of emotions and cognitions about the emotions, both one’s own emotions and the emotions of others. Meta-emotion refers to the idea that whenever we elicit a certain emotion, we also deal with subsequent emotions regarding how we experienced the primary emotion. While some psychologists have examined the influence of meta-emotions on how individuals interpret and deal with their own and others’ emotions, much of the literature regarding meta-emotion has focused on how parental meta-emotion impacts the social-emotional development of their children."
Example from emotion-regulation and heart-rate recordings:
Children's emotion regulation: Self-report and physiological response to peer provocation. Hessler, Danielle M.; Fainsilber Katz, Lynn. Developmental Psychology 43.1 (Jan 2007): 27-38.
.....Seventy-two children in middle childhood (average age = 9 years) participated. Time-locked measures of heart rate reactivity and recovery were obtained in response to provoking comments, and vagal regulation was measured throughout the provocation session. Children who reported greater dysregulation showed increased heart rate reactivity to provocative comments (i.e., steeper heart rate slope) but no difference in heart rate recovery. The context-free but not the context-specific self-report measure was associated with a failure to suppress vagal tone. Implications for ER measurement and children's peer relations are discussed.
This review can give you some ideas:
Methodological implications of the affect revolution: A 35-year review of emotion regulation assessment in children. Adrian, Molly; Zeman, Janice; Veits, Gina. Journal of Experimental Child Psychology 110.2 (Oct 2011): 171-197.
Overall, 61.1% of published ER articles relied on one method and 23.6% used two methods. Analyses revealed (a) 82.8% of published ER research occurring within the past decade; (b) higher rates of observational methods with infant and toddler/preschool samples, but more use of self-report methodology with middle childhood and adolescent samples; (c) a longer history of published ER research with samples of infants to 5-year-olds, including the use of more longitudinal design, compared with older samples; and (d) a positive association between journal impact ratings and the use of physiological and observational measurement. Review of the measurement tools used to capture ER revealed great diversity in how emotion processes are understood and evaluated
Another paper:
Meta-emotions as predictors of drinking to cope: A comparison of competing models. Shaver, Jennifer A.; Veilleux, Jennifer C.; Ham, Lindsay S.. Psychology of Addictive Behaviors 27.4 (Dec 2013): 1019-1026.