Maybe this article will help you:

http://www.nature.com/ngeo/journal/v4/n11/abs/ngeo1297.html

Eutrophication has been shown to enhance acidification of coastal waters. One thing I feel we must be clear on is that there needs to be a distinct, defined difference between ocean acidification and coastal acidification. The open ocean is not subjected to many of the processes that coastal waters are subjected to and is therefore influenced more by anthropogenic CO2 than coastal waters are.

With that said, studies have found that eutrophic conditions can enhance the acidification of coastal areas. The increase in algal production and subsequent increase in microbial activity both reduces O2 and increases CO2, creating more acidic conditions. This may not be all that eutrophication does with respect to acidification, however. For example, using model simulations, Cai et al. (2011) found that coastal waters were more acidic than expected from human-induced acidification and eutrophication alone, suggesting that eutrophic conditions may reduce the buffering capacity (against declining pH) of coastal water and contribute to a more severe degree of acidification. Furthermore, Salisbury et al. (2011) found that river discharge enhanced the acidity of coastal waters by delivering acidic waters (produced, in part, through terrestrial human activity) to the surrounding habitats where they empty.

Other studies have shown similar trends, with eutrophic conditions contributing to pH declines in coastal areas (e.g., Borges et al. (2010); Feely et al. (2010)).

Here are links to the above-mentioned papers:

Cai et al (2011): http://www.nature.com/ngeo/journal/v4/n11/full/ngeo1297.html

Salisbury et al. (2011): http://onlinelibrary.wiley.com/doi/10.1029/2008EO500001/abstract

Borges et al. (2010): http://orbi.ulg.ac.be/handle/2268/34336

Feely et al. (2010): http://www.sciencedirect.com/science/article/pii/S027277141000185X

Hi

Eutrophication is also causing large CO2 inputs into coastal waters. Eutrophication fuels massive algal blooms, & when organic matter from these blooms is respired by bacteria, O2 in the bottom waters get depleted and add on to CO2. These CO2 inputs may decrease the ambient pH values, effects that may increase with decreasing temperature and salinity.

Please read on:

http://www.ncbi.nlm.nih.gov/pubmed/22889106

Consider the amount of CO2 assimilated by producers-say phytoplankton. It can then be passed on as food to various consumers but majority of them leads to their natural death.Till it is totally disintegrated by bacteria,it may be consumed by various filter feeders or become deposits & may be later sedimented.Hence all the CO2 assimilated during its growth in case of say a single plankton,will not be totally given out to environment due to the above processes.Even if it has a chance,it will take a very long time to do so. Eutrophication gives out Oxygen which shifts the pH of water towards alkaline side,which will annul the effects of acidification.Hence acidification has no effects on eutrophication,due to the above reasons.

To the best of my knowledge of the problem (which is rather limited), ocean acidification should alleviate carbon limitation under conditions of excessive nutrient supply typical for coastal regions that experience eutrophication. Therefore, at first, the increased carbon loading that generally leads to acidification is likely to increase both the primary production and growth of most phytoplankton species. The sinking of the organic matter will then increase the level of bacterial activity at the bottom, releasing the stored carbon and consuming the oxygen. It remains unclear if these two processes will balance each other. Most likely the dynamic of the increased primary and the bacterial production will increase under ocean acidification. Because of this complexity, the question should rather be stated in terms of potential effects of ocean acidification on the dynamics of these two process in typically eutrophic regions of the ocean. I don't think there is enough knowledge yet to answer the question as originally stated.

In addition to the comments posted above, utilization of nutrient via riverine runoff or atmospheric input by phytoplankton, subsequent sedimentation followed by remineralization make high CO2 world in the benthic environment of the eutrophic coastal region. After making the acidic waters beneath the surface, physical condition may be able to control the acidity of the surface. The effect will accumulate in response to the amount of nutrient deposition and residence time of certain water mass.

References listed by Jeff Clements are very useful to understand!

Is enhanced oceanic CO2 sequestration leading to eutrophication . I believe this is the case in Arabian Persian gulf coastal waters