The only way that is possible is if you get a letter which gives power of attorney to the other person. This must show medically that you are incapable of applying for the passport yourself for reasons of mental incapability, physical disability or emotional disability(very hard to prove).
The reason you must apply for a NEW passport in person is so that the Gardai can sign off on your pictures and birth certificate/other ID that it is actually you.
Sending in a friend/relative you say "howya, will you stamp this" will not really do.
If it is a replacement passport then you can just sign the form and submit the new pictures and the old passport in the post office and bobs your uncle you will get a replacement.