May be the answer is that you'd better not try. THe ecosystem service metaphor is helpful to understand interdependances between societies and ecosystems at appropriately agragated level. It is poorly defined for a single species, even for flagship or keystone species. Good luck.
I guess the correct answer depends markedly on the type of service you're trying to assess. While it should be relatively easy to assess a 'provision' service ( eg wood or timber production) even for a single species, other services require an interaction between species within ecological communities. In that case, isolating one of the species of the community out and relating the service (or a share of the service) to this species alone is either impossible or irrelevant, because it overlooks the interactions. So for this type of services, Jean Michel's answer is probably the correct one.
For this you will have to see various parameters like type & amount of nutrients taken up by the plant body,amount of biomass given out in unit amount of time,inter-relationship with various types of animals & plants,amount of CO2 used & O2 given out per unit time during seasons,growth rate to name a few.
Though some of the parameters to assess is taxing,but if you start you will definitely end up with concrete results, as researchers are supposed to be optimistic at all times.
It really depends on the location of the species and in which area of ecosystem it is really serving. But as others have pointed out that if it grows in a mixed forest then the interelating part of offering a single service will be complex to evaluate at single species level. If its a residential landscaping species then you could relate to housing prices with and without the specie. If its in a park then you may use park user perception without the species. If its in the forest then probably use Trivedi's suggestion. Again you will expect alot of critism because most methods seem to neglect the inter-relating functions amongst different species to offer a single ecosystem service. All the Best.
as stated previously, the concept of ecosystem service is a metaphor that we developed to understand the welfare that people from nature. You may look some concepts of functional diversity, and you will find that the relation between diversity and ecosystem services if full of caveats. Because of this, you may want to focus on a specific ecological process of your interest, an measure the contribution of the species.
Ecosystem service of an individual species may probably be studied in a monoculture taking into consideration the effect of age, but to attribute this to a given species, you might need to compare to some sort of control. As mentioned by others, for some ecosystem services, such a study is better made at ecological than species level.
I think we need to turn this question around, like I have at https://www.researchgate.net/post/Do_we_need_to_set_aside_35_of_the_planet_as_Ecological_Restoration_Preserves?
I have estimated that we need to maintain at least 35% of the natural ecosystems intact as a good starting number, but it might be as high as 50% to keep the annual rainfall flowing at a regular rate each year in India, parts of Africa, etc..
Sitting writing this answer in drought-ravaged California, rainfall seems to be the most important short-term "Ecosystem service" we depend on for our day-to-day survival--we need the normal rainfall to fall this month wherever we live, or are we going to get droughts or floods caused by our mismanagement of the natural systems?
Your answer is not quite an anwser to the original question!
As to rainfall, not quite sure it can be regarded as an ecosystem service. This would mean that ecosystems are per se the cause of rainfall. My (climatology layman's) understanding of water cycles is that rainfall depends primarily on many things way beyond single ecosystems ( like general air movement, topography, latitude, proximity to the seas/oceans, etc...), although I agree that rainfall conditions the way these ecosystems are set up and therefore function.
I do not think the original question here can be accurately answered, even though it is a popular topic of discussion to try and estimate an economic value to "Ecosystem services", That line of question misses the point, that all of our societies are directly connected to the health of the natural ecosystem around us.
A good example of our rainfall being dependant on the local ecosystems, happened in what is now Pakistan about 4,000 years ago. A massive Indus Valley Civilization built 1,000 cities by cutting down the Pseudomonas-host trees in the area to fire the millions of clay brick they built their cities from.
Cut down and burn the Pseudomonas host trees, you take away the Pseudomonas, and you eliminate the rainfall, and then you must abandon your 1,000 cities, and those site stay abandoned for the next 1,000 years, and your civilization is not even discovered that you ever existed, until 1922.
Fortunately we just found out about the Pseudomonas, and just in time before we cut down the last host-trees in India for example. in the Western Ghats.
Also, we are just finding out about the 5,500 year old Pakistan-Arabia Dust Cloud, that can cause droughts from India to Arabia in wherever lands it inhabits. Fortunately since it is man-made, humans can cause it to disappear and bring rain fall again in areas that before the Dust Cloud had lakes and flowing rivers like the Empty Quarter of Arabia.
We allowed our domesticated animals to create Mars-like barren areas that produces the Dust Cloud each year, and by replanting the native grasses and the Pseudomonas-host trees, then we can really see and measure how much the natural ecosystems contribute their "Ecosystem services" to human survival--that they are essential.
So then the next step--especially with the Pseudomonas-hosts--is how much cover do we need to sustain our human-occupied portion of the planet? That is where I am suggesting at least 35% cover of high quality natural ecosystems.
The main thing is that see the ecosystem where your species should live, and after see the importance of your species in the food web where she involved
and after that you can the ecosystem services for your species