Is there a way to treat manic depression without taking psychiatric medications?

Not generally. There are times when a manic person is so severely psychotic and grandiose that medication is not enough and shock therapy is used. Even then medication is required. Left untreated manic depressive illness can be fatal for a number of reasons such as suicide, severe risk taking behavior and accidental fatal overdoses of medication, street drugs or alcohol. Risks are high doing nothing.
Types of Bipolar D/O. A simple answer would be no but it is important to elaborate. Bipolar disorder has numerous tyes and sub-types. Many times hypomanic and subtle depression may go on for long time before manifesting to full blown picture requiring medicine. As a general rule without treatment the symptoms will become more severe, frequent and interfere with functioning.
Bipolar depression. Basically no. If left untreated, it may even get worse and lead to worsening of depressive symptoms and possible suicidal thinking. Although various treatment options may be used for management of bipolar depression, the medications are the first line treatments. Two mood stabilizers/antipsychotics that are fda approved for acute management of bipolar depression are serouquel and symbyax (fluoxetine and olanzapine).
Yes. Mild to moderate depression can be treated with psychotherapy, healthy diet, exercise, and avoiding alcohol and substance use. Depression associated with thoughts of suicide, psychotic symptoms or significant impairment in daily functioning do be evaluated fur treatment with medication.