You can largely reproduce the Stability API using the top BigQuery query on this page: https://blog.gdeltproject.org/assessing-turkeys-physical-stability-and-societal-mood/ and the second query there shows you how to use the emotional data to generate emotional timelines indicative of various stability undercurrents. Note that the second query, the emotional query, will consume a LOT of data and so you should use the partitioned GKG table and limit your query to just the time period you need, or just stick with the event query to start with.
SELECT substr(string(DATE),0,8) as daydate, count(1), avg(float(REGEXP_REPLACE(V2Tone, r',.*', ""))) tone
, avg(float(REGEXP_EXTRACT(GCAM, r'v19.1:([-d.]+)'))) anew,sum(integer(REGEXP_EXTRACT(GCAM, r'c8.3:([-d.]+)'))) ridanxietycnt, sum(integer(REGEXP_EXTRACT(GCAM, r'wc:(d+)'))) wordcount
FROM [gdeltv2.gkg]
where V2Locations like '%Turkey%Turkey%'
group by daydate