Congrats on your venue choice for your honeymoon! 

Info on Tolls -- http://etoll.ie/driving-on-toll-roads/information-for-visitors/

The M50 (Ring Road around the West of Dublin) is a Barrier-Free Toll, located North of Junction 7 (N4 Lucan).  This Toll must be paid at any Payzone  location   http://www.payzone.ie/

It can also be paid online, at:     www.eflow.ie        or, by phone.  Toll for a passenger car is 3.20 Euro, but check with your Car Hire Company to see if they have a Transducer (Like a US EasyPass or Florida SunPass) -- and, if it is Automatic, or optional (as they usually charge a 'Service Charge' for the "Convenience".

All other tolls have payment booths.  Generally speaking, there is only one toll Booth per motorway -- However, that is NOT to say that they are Single Toll.  For example, Driving from Dublin Airport to Galway,  You'll pass through the M50 Barrier Free Toll, before turning onto the N/M4.  Just past Junction 8, you'll pay the M4 Toll (2.90 Euro), an Exit or so before you turn off, onto the M6.  Then, about 18 Km beyond Ballinasloe. you'll pay the M6 toll (1.90 Euro).

Likewise, a Drive from Dublin Airport to Cork will include the M50, M7 (1.90 Euro) and M8 -- Fermoy Bypass (1.90 Euro).

As to Rental Cars, the Thread was started in 2009, but the newest posts are from this month.  It's a lot to 'wade through' but we make every attempt to keep it current.  Lots of folks here have had good luck with Dan Dooley and a few members (That always buy Full Insurance) have said good things about Easy Tour ( a Hertz Agent).  I believe Michele recently utilized a Dooley agent on her latest visit.  In my last 4 visits, I've used Dooley twice (2012, 2016), Hertz, for two different rentals in 2013 and Avis, once -- in 2014.

For the last few years I've used Dooley, Avis and Fox.

M50 rules: https://irelandyes.wordpress.com/2013/03/02/how-to-pay-your-dublin-m50-motorway-toll/