Can easy-bruising be a side effect of either methimazole or propranolol? or both? or neither...

Possibly: Easy bruising suggests a problem with clotting which can be due to a variety of causes from decreased platelets to problems with the clotting pathway. Methimazole has a few less common but serious side effects which include a decrease in white blood cells (agranulocytosis) and blood platelets (thrombocytopenia). I would have this assessed by you doctor as soon as possible.