The COVID-19 pandemic has had a negative impact on the mental health of the population. Many studies reported high levels of psychological distress and rising rates of suicidal ideation (SI). Data on a range of psychometric scales from 1790 respondents were collected in Slovenia through an online survey between July 2020 and January 2021. As a worrying percentage (9.7%) of respondents reported having SI within the last month, the goal of this study was to estimate the presence of SI, as indicated by the Suicidal Ideation Attributes Scale (SIDAS). The estimation was based on the change of habits, demographic features, strategies for coping with stress, and satisfaction with three most important aspects of life (relationships, finances, and housing). This could both help recognize the telltale factors indicative of SI and potentially identify people at risk. The factors were specifically selected to be discreet about suicide, likely sacrificing some accuracy in return. We tried four machine learning algorithms: binary logistic regression, random forest, XGBoost, and support vector machines. Logistic regression, random forest, and XGBoost models achieved comparable performance with the highest area under the receiver operating characteristic curve of 0.83 on previously unseen data. We found an association between various subscales of Brief-COPE and SI; Self-Blame was especially indicative of the presence of SI, followed by increase in Substance Use, low Positive Reframing, Behavioral Disengagement, dissatisfaction with relationships and lower age. The results showed that the presence of SI can be estimated with reasonable specificity and sensitivity based on the proposed indicators. This suggests that the indicators we examined have a potential to be developed into a quick screening tool that would assess suicidality indirectly, without unnecessary exposure to direct questions on suicidality. As with any screening tool, subjects identified as being at risk, should be further clinically examined.