This is a role that requires a lot of creativity, since it is a department that is often under exploited in sims. Due to this, there can often be a sense of isolation compared to what the other departments offer. You have no crewmembers to heal, labs to run or engines to maintain. As a diplomat, your function is to understand the sector where your ship/starbase/colony operates.
What other species live in your sector? Do they have specific rituals or cultural traits that would affect negotiations? How do these species get along together? Has there been any conflict between them in the past?
Also, what's the economic landscape like? Who are the main powers in this sector, and what are their positions regarding Starfleet?
Some of this info will exist within Star Trek lore, but in many cases you'll have to invent those relationships and keep tabs on the alliances and rivalries that you've created.
Adding to the sense of isolation, because so few players choose to portray a diplomat, you will often be the sole person in diplomacy. Whether you are the head of your department or not, you need to give life to diplomacy. Create aides, secretaries and special guests who will make it easier for you to get into your role.
Before the mission
Because not all missions focus on diplomacy, you often have to create your own material. Once you have a fair idea of the political atmosphere in your sector, you need to find your way into the plot, and enrich it with background information. Are there any sign of trouble between the various species that inhabit the sector where you operate? Signs of unrest, economical difficulties?
You need to build on those aspects and create plausible conflicts that will feed the ongoing plot, and also give credence to your character. If your input is going to have dramatic consequences on the mission, be sure to check with your C.O and F.O. that what you have in mind to do will fit with the way the mission is going.
Also, when the roles are attributed at the start of a mission, you might get the opportunity to write with other diplomats (often MSNPCs), which will help you develop your skills as a diplomat.
During the mission
This is where you get to develop the relationships between the different species that exist in your area of space.
Being a diplomat is all about expressing yourself and promoting not only the Federation's image, but also the goals set out by your C.O.
After the mission
This is the time to reflect on what has happened during the mission and how those events are likely to affect the sector in the future. Your role as a diplomat gives you a chance to bring the sector to life, covering aspects of the game that other players wouldn't think of. To make this easier, don't hesitate to describe meetings between various species and keep your character up to date with the situation.
CDOs negotiate treaties, attend to official meetings, mediate relations between several governments. They also represent the interests and policies of the Federation.
A convincing CDO has to be good manager, a resilient negotiator and a respected representative of the Federation. A CDO also coordinates the activities of his/her staff. However, as it is with other departments, it is best to give your staff some leeway. Give your character some specializations, and encourage players within the Diplomatic Corps to do the same. This might even create some interesting subplots. However, any idea that could seriously impact the economy and politics of your sector of operation should be discussed beforehand with your C.O and F.O.
Here are a few specialization ideas:
Economic (Econ) Officers: they fund scientific advances, protect the environment, or negotiate new trade laws.
Management Officers: they are action-oriented “go-to” leaders responsible for all embassy, consulate, or diplomatic mission operations from real estate to people to budget.
Political Officers: they keep the CDO up-to-date on political events and changes occurring in space.
Public Diplomatic Officers: they build mutual understanding and support for Federation policies by being in contact with foreign dignitaries. They work with traditional and social media; educational, cultural and sports programs; and all manner of people-to-people exchange."
Consular Officers: their primary job is to assist and protect Federation citizens living on non-aligned worlds. If you find yourself in trouble in those territories, you’ll need the help of this officer.
Furthermore, all diplomats listen to and observe what is going on in their sector of operation. They analyze the situation, and report their conclusions to the command staff.
As a head of department, a CDO is also responsible for any mishap that might happen because of decisions taken by his/her staff. With diplomacy dealing with events and circumstances happening in space, any mistake could have serious ramification, and would need to be corrected with the utmost care.
In case of doubt as to how to handle delicate situations, it can be useful to search Memory Alpha, and check how certain conflicts have been resolved in Star Trek. This will also bring some added credibility to the way your character addresses the dispute.
To conclude, there is a lot of things to take into consideration when playing a CDO. Due to this, it is a role that might not afford as much freedom as one might have first thought. To add to this, it is also a position that few players go for, so there aren't many examples in the Fleet of what can be achieved in this field. Yet it is this very scarity that makes it an ideal role for creative minds. The path is pretty much open, and if you take up the challenge of bringing some life to the diplomatic department, it is up to you to define how negotiations are to be handled, and what species you choose as your privileged allies. Those two elements alone are sure to influence the atmosphere of the sim where you play.