Are there any actual medications that will reduce someone's suicidal ideation?

Yes. However, this is a complicated question because many factors can contribute to suicidal ideation. Brain diseases like bipolar disorder and depression greatly increase the frequency of suicidal ideation and the % of completions. Personality issues may contribute, and social stress, financial stress, loss of self-esteem and confidence are often important factors to address.
Yes. If someone has a depression severe enough that they consider ending their life, then there are antidepressant medications that can improve their mood and help them move to a more hopefulpostion. Meds are seldom enough. Many other things are helpful, nutritional deficiencies and starvation can result if si also. 1/2 hr of exercise dailey is as helpful as any medication.