What were the traditional beer styles of Ireland (before Guinness came to dominate)?

The question is how traditional are you talking about? The rise of porter/stout took place in the 1800's and hops came in hundreds and hundreds of years before that. Styles of beer are constantly changing all of the time so there is no one "traditional" beer just different snapshots of a constantly changing way of brewing.

To take Guinness for an example, the recipe for Guinness has constantly changed. Brewers tweak the recipe year by year, often for economic reasons. For example the world wars often made it hard for Guinness to get a good supply of brewing ingredients such as malt and made things even harder for brewers in the UK and changes in taxation made brewers adjust their recipes to try to avoid as much tax as they could. The British Whitbread brewing company bought the competition's beers every year to analyze them and keep tabs on the competition and Ronald Pattinson (an amateur historian who has done an absolutely mind-blowing amount of original archival research on brewing history, including learning several languages to be able to read the records to additional countries' brewing archives) gives you the numbers from the Whitbread archive on Guiness here: http://1.bp.blogspot.com/_CHrKKDU9290/RvezsCi_f3I/AAAAAAAAAaM/iMQur9DgtY0/s1600-h/Guinness_1896_1982.jpg

As you can see the simple things like how much alcohol there was in a Guinness Extra Stout jumped around wildly from year to year. If you took a time machine and sampled one Guinness from every decade you'd see absolutely massive changes in the taste of the beer, with the ones from the 19th century being pretty much unrecognizable compared to a modern pint of Extra Stout.

Two big discoveries utterly transformed the taste of beer in the 19th century, including in Ireland. One was the isolation of specific yeast strains by the Carlsberg brewery (see: Hansen, E. C., & Miller, A. K. (1896). Practical studies in fermentation: Being contributions to the life history of micro-organisms. London: E. & F.N. Spon.) before this brewers yeast was a mix of all kinds of different strains and even species of yeast (especially brettanomyces yeast, which are very rarely used in commercial brewing these days, although it is making a bit of a comeback). Because of this wild mix of yeast you'd have a much less "clean" taste and instead something much more flavorful and unpredictable. Brett yeast specifically produce some bizarre flavors and aromas, with "horse blanket" being a common description (see here: http://www.milkthefunk.com/wiki/Brettanomyces).

The other big change to brewing the 19th century was the use of a hydrometer which began in Britain in the late 18th century and began to have powerful impacts on brewing in the 19th century. This is a device for measuring how dense beer it (which is called the "gravity" of the beer with "original gravity" how dense it is before fermentation and "final gravity" how dense it is after fermentation). This is important since wort (wort is unfermented beer) becomes less dense as it ferments so you can use a hydrometer to measure how much alcohol is in the beer. What brewers discovered when they started using hydrometers was that they were getting far more maltose (the stuff beer yeast eat) from lightly roasted malt than darker malts. At this time lighter roasted malt ("white malt") was more expensive than darker malts but it was so much more efficient at producing alcohol that brewers switched over to it to save money. This lead to problems in that people wanted darker beers and at this time people mostly used just one kind of malt (so a "single malt") to make beer and if you're using just light malt you won't get dark beer. And people wanted dark beer! So what brewers ended up doing is having the vast majority of the malt be lightly roasted malt and then a tiny percentage be burned black which was enough to turn the beer black. This is how most dark beers are produced these days and resulted in a huge shift in the way that beer tasted. Seer: James Sumner. (2001). John Richardson, Saccharometry and the Pounds-Per-Barrel Extract: The Construction of a Quantity. The British Journal for the History of Science, 34(3), 255-273

Before that the biggest impact was the use of indirect heat so you could get beer that didn't taste smoky. Before that was the use of hops. Before that was having a metal pot so you didn't have to throw hot stones in water to heat it up. And on and on back in time. Brewing never stood still.

But to answer you question really quickly there's nothing especially traditional about modern Irish Red Ale.

If you want something REALLY traditional you'd have to do something like:

Mix a whole bunch of different kinds of yeast together and hope you have the right mix. Throw in a bit of yogurt for a touch of lactobacillus.
Get strains of barley that nobody farms anymore.
Malt them on the floor and then put them on a board of wood with a bunch of holes in it and light a fire under the board.
Grind the malt.
Cook the grains a bit in a big pot at the right temperature. Good luck getting the right temperature without a thermometer.
Dump the grain soup out over some spruce boughs to strain out the grains.
Dump in the yeast mix.
Let it brew only a short time, less than a week so it's still a bit sweet.
Drink it all down in a big feast. It'll be thick and goopy with only tiny bit of carbonation with a bit of smoke and bacterial tang and spruce and taste funky as all hell but probably pretty good and NOTHING absolutely NOTHING like what you can buy commercially most anywhere in the world.