In response to your question regarding whether or not the spouse of a NI citizen would be entitled to apply for Irish citizenship - you might answer the following. Before I go on however, whether or not this spouse will be entitled to apply for UK citizenship on the basis of you being born in Northern Ireland is a matter for the UK authorities only. Citizenship matters are always a matter for each national government.
To find out whether or not or not your spouse may be entitled to apply for Irish citizenship on the basis of their marriage to you - you might answer these questions:
1. Where is this spouse from and what is their nationality?
2. When were you married? (Remember, it is not possible to claim Irish citizenship through marriage if you were married after 30 November, 2002). Instead, your spouse may apply for Irish citizenship through naturalisation but with more favourable terms than the normal naturalisation requirements).
3. Where are you both currently living (i.e., in the Republic of Ireland or abroad)?
If you can answer the above 3 questions, I'll be happy to provide more information.
Alternatively, there is a wealth of information pertaining to Irish citizenship through birth, descent, marriage and naturalisation on the Oasis website.