Granted, that's a pretty tall order. Ideally, we would reduce the atmospheric CO2 from ~400ppm (where it's out now) to 200ppm (where it was before the whole industrial revolution began). At the very least, we probably want to reverse the current trend of +2.0ppm / year to (say) -2.0ppm / year, so hopefully we skim under whatever the wire is.
Some researches claim that the Little Ice Age was caused by the reforestation of the Americas after Europeans accidentally killed all of the Americans who were keeping the content pretty clear of trees. [1] It is estimated that reforesting the Americas sucked about 6ppm to 10ppm of CO2 out of the atmosphere.
So one way to suck CO2 out of the atmosphere is to grow a lot of trees (or other plant life). And then do that every year for about a century; it's not enough to simply reforest even the entire world once, because that would probably only suck (say) 20ppm of CO2 out of the atmosphere, a mere tenth of the target. So after you grow your primordial forest, you need to chop it all down, bury it (or do anything else with the wood that doesn't release its carbon back into the atmosphere), and then plant a new forest, and keep doing it over and over again for however long it takes to get the atmospheric CO2 levels to where you want them to be.
So it's possible to counter ocean acidification, and maybe not even that hard (hell, you're even creating a bit of a "wood rush", since you're going to have lumber coming out of your ears by the time you've regrown enough trees to cover the world ten times over), but I don't really see it happening.
ETA: Based on the figures for tree productivity [2] it looks like you'd need to add about 90 million square km (5% of the Earth's land area) of forests operating at peak productivity to go from +2ppm to -2ppm atmospheric CO2.
[1] http://phys.org/news/2011-10-team-european-ice-age-due.html [2] http://www.safnet.org/answer/kids_corner.cfm
1) There is no consensus as to whether it was global or just hemispheric and
2) At least in Europe, it was well underway by the 1200's, so the timing with that theory is off.
2) You're confusing the end of the Medieval Warm Period with the beginning of the Little Ice Age. The Medieval Warm Period ended in approximately 1250 AD; the Little Ice Age began in approximately 1550 AD. While it is possible that the two events are related, there is no reason to assume they are.
I'm still unsure about the appropriate process of dealing with all the CO2 released over the last ~200 years - it originally came from somewhere, I'd imagine likely the atmosphere - then over millions of years it was sequestered into the earth through coal and oil. And we've undone that sequestering in a very rapid manner, over approx 200 years, an instant in geological terms.
I'd say the hammer stroke hasn't even started ringing yet, and we haven't even begun to see the changes that we've unleashed - and who knows what they might be? So many unknown unknowns there... and we're attempting to throw our best minds at it, yet we're also still very much continuing with our current trajectory.
I understand there are always risks to sticking our fingers into something we don't understand well. But those risks have to be weighed against the risks of inaction, which seem in this situation to be quite substantial.
I suggested sodium hydroxide because adding sodium ions to the ocean is obviously benign. Seems to me the greatest risk from doing this is that the concentrated alkalinity will kill marine life before it disperses. I don't know whether that's a show-stopper.
I also haven't penciled out the numbers to see how much NaOH would be required, and how that compares to current world production. I have no idea whether this is practical. But I think we should be asking these kinds of questions.
Still, it is complex and scary, and I have had better success by increasing flow and surface agitation for better oxygen exchange. Just like I would prefer to have less CO2 in our atmosphere.