Applying for Irish Passport - No U.S. Birth Certificate

My father was born in Ireland and I am an Irish citizen by virtue of his birth in Ireland - although born in the U.S. (My parents never married and my mother returned to the States to have me in the 1950's.) Apparently, for social reasons, she never never registered my birth properly with the State.

I have a U.S. passport because (in the U.S.) - you can obtain a certified "Letter of No Record" from the State you were born in - and provide supplementary documentation to prove your citizenship. On the basis of that documentation, I was issued a U.S. Passport.

However, I must submit a Long-Form Birth Certificate with my Irish Passport Application. I have my father's birth certificate - but has anyone here had experience with alternate documentation of Irish parentage OTHER than a Birth Certificate?

Thanks in advance for any assistance you can provide.