My father who is 87 years old is finding it very difficult to perform Amavasya Tharpanam each month.

Anser:  In such cases one can perform the Tharpanam through a third person (who himself should be a person performing thrapan for his pithrus) by authorizing/giving the dharbam (kaippil). The same will be done in your fathers presence and your father would pronounce the names of his ancesters while the authorised person does the tharpan. And the person who takes just like power of attorney (kaippil) should be compensated suitably. If one is speach disabled condition, then also the third party can perform but only in his presence and after taking the kaippil on his behalf.