Black spots  on leaves are not a sign of fireblight, but rather Pear Scab. Unlike fireblight, which is a  disease  treatable in early stages by a careful program of spraying, Pear Scab is a fungus. It is preventable by careful raking up and removing fallen leaves as the tree goes dormant in the late fall and early winter. Its main symptom is velvety looking black spots on the leaves. It tends to occur when newly emerged (and emerging) leaves are wet from rain  showers or sprinklers for more than 10 to 24 hours. The spots emerge two to three weeks after the wetting. Left untreated, it will spread to bark tissue and cause cankers as well. You can prevent this fungal problem by spraying in the dormant season with an anti-fungus product such as lime-sulfur. Sprays at this point in the year may help: Consult the labels on anti-fungals for information as to whether or not emerging fruit  would be harmed by the sprays. (A savvy salesperson  may also be able to provide information; consulting a nursery that sells fruit trees may be your best source about specific products.) And be sure to follow  this year's cycle by carefully cleaning up any fallen leaves in fall and following a program of  dormant spraying aimed at preventing fungal disease.

Fireblight "acts" entirely differently from your problem. it does not start out with black spots on leaves: it is more likely to be a disease that enters the plant through an injury and attacks the bark. it oozes sap and forms "cankers" (large roundish outbreaks in the bark) Your old pear should be removed. There are newer fireblight resistant varieties on the market. fireblight  affects mainly bark; the tree will die out in partsl as the disease sprea

You' are very welcome. Hope you can find a replacement for the old tree. Make sure it does have resistance to Fireblight! And be sure to spray your other tree as needed.  Marjorie