Hyperthyroidism on methmiozole pulse fast afternoons into evening then pulse rate drops to 79 midnight to noon BP which beta blocker is best for pulse?

Class effect. Most beta blockers will lower the pulse rate ( heart rate)- this is considered a class effect; however, certain beta blockers are stronger than others in slowing a rapid heart rate-consult your physician.
Yes. beta blocker can control your pulse better until the thyroid function is under control.