Are there effective alternative therapies for child with low thyroid?

No: No effective alternative treatment is available other than replacing the deficient thyroid hormone.

??????: If you mean nonprescription treatments or supplements, there are none. If needed, proven treatments are just that, proven to work.Do not risk your health over quackery.

No: If a child is not manufacturing enough thyroid hormone it must be replaced. Levothyroxine is the generic name for the medication used to treat an underactive thyroid. Particularly in children, thyroid hormone is important for growth and also brain development when very young.

Only thyroxine: Only thyroxine (synthroid, Levoxyl or levothyroxine) is considered the most effective and safe way for the treatment of hypothyroidism (low thyroid state). Exception to the rule is when certain medications are used that can interfere with thyroid function (such as lithium), selenium deficiency or obesity induced TSH elevation, all of which will need different approaches to restore thyroid function.

Alternative therapy: Be careful of "alternative" therapies. I'm all for natural remedies when those exist, but synthetic thyroid hormone is safe, effective, and has almost no side effects. It is a proven drug over decades of time. Im not aware of any other alternative.