Orions were discussed over the last days as possible antagonists in a thread over here.
For other ideas:
During TNG, the Orions are portrayed, essentially, as some kind of space-Mafia. Depending of your style of game (and the PC’s connection to their culture) you could do all kinds of plots: interfere in armed robbery, protection rackets or slave trade, investigate crimes committed by the syndicate (e.g. uncover that a tragic accident was actually a murder committed by a syndicate – but why?), maybe leading to hunts for missing/abducted persons. Maybe the mission is to infiltrate a cell of the syndicate to obtain information, contraband, or both.
You can combine this easily.
Just off the top of my hat:
Mission 1: Accidents
Suggested Spotlight Role: Captain or First Officer
Synopsis: Investigating the disappearance of a team of independent scientists lead to uncovering a plot by the Orion Syndicate.
Opening Log Entry: We have been sent into the Xintana System. The inhabitants of the fourth planet, the Vellathra have recently acquired warp travel and were sent an independent science team as liaison. Communication with the team fell silent a few days ago for no apparent reason. We are to investigate.
Major Beats:
- Break the Silence
Not only does the science team not answer – no one answers the players hails. Scans, however, will reveal that everything’s normal on the planet. The science team can, however, not be located. After a while, Vellathran authorities will order the ship to immediately leave the system, providing no reason for the abrupt termination of all communication. On the players refusal, small battle ships (that are no match for the players) will try to attack. The players will have to convince the Vellathran authorities to at least talk with them.
- Working Out the Problem
The players will find out that the science team was placed under arrest and is currently accused of treason and murder. The team advised a group of Vellathran scientists to refine the already existent Vellathran transporter systems to make them safe for the transport of living beings with great success – until a series of transporter accidents killed several key figures of the Vellathran society, including polititians, scientists and even artists. The systems were clearly manipulated and the foreign scientists are under suspicion. The authorities, however, will release them if proven they are not responsible for the accidents. Possible solutions will include criminal investigation and engineers taking apart the transporters for diagnosis.
- Chase
The transporters were indeed sabotaged – but not by the foreign scientists. Indeed, one of the Vellathran scientists carefully planted evidence pointing at the team while commiting the murderous acts all by himself. When the players are just about to reveal him, he flees – with a small ship full with technology far beyond the Vellathran capabilities. The players have to chase him down and make him confess to the Vellathran authorities to get back the science team.
Minor Beats:
One member of the team is a Klingon and also his governement wants him back. During the negotiation with the Vellathran or the investigation of the “accidents”, a Klingon vessel arrives, demanding extradition of the Klingon scientist. The players will have to convince the Klingon captain to wait until the investigations are finished – or they will need to hurry up. To make things worse, the Klingon might decide to simply destroy the ship of the fugitive murderer, which is clearly not in the interest of the players and/or the science team.
Key Non-Player Characters are missing in this spontaneous Mission Brief, but there will be ample supply within the rules. Just pick some very small ships / shuttles (scale 1 or 2) for the fighters, a scale 2 or 3 ship for the murderer, a medium-sized Klingon ship and some polititians/ambassadors/diplomats for the other NPC. The murderer could be a specialised scientist or you could adapt a Section 31 operative. 
Conclusion:
Even if the fugitive murderer is dead, the technology of his ship alone will tell that there were outward interference in the Vellathran transporter systems. If he is caught alive, he will confess to have been paid for his acts of sabotage by a certain “Navras” whom he knows little about or decides to keep silent on. In either way, the science team is set free. Relations between the Federation and the Vellathran authorities, however, will be damaged.
Adapting this Mission to your Campaign:
Obviously, there can be further missions to re-establish good relations between the Federation and the Vellathran. If the group decides to investigate “Navras”, they will find that the shuttle of the murderer is a jury-rigged pile of technologies most different in origin. Prominent parts (e.g. propulsion system and/or shields, maybe weapons?) will be Orion in Origin. Also, close scrutiny of the sabotaged transporters could give hints at Orion involvement.
In TNG era, the Klingon scientist might also be a Romulan; in ENT era, replace the Klingons by Vulcans.
In Mission 2, make the murderer’s ship and/or the devices he used the A-plot, best investigated by the science officer and/or the chief engineer. The players will find out Navras’ affiliation to the Orion Syndicate. Maybe there is time pressure as the data storage cores of the ships may deteriorate quickly due to security / self-destruct devices. Maybe heavy encryption has to be broken or the channel of communication relies on a certain vector to the Xintaran star, so it can only traced back if the players are back on the Vellathran surface in the murderers laboratory.
Minor beats could include a member of the team of scientists being traumatised, needing attention of a counsellor. Or the team was put under “harsh interrogation techniques” (i.e. tortured) and one ore more of them needs medical treatment.
In conclusion, make your players find out that Navras is most likely an operative (either male or female, pick your favourite) of the Orion Syndicate, trying to undermine good relations between the Federation to keep the Vellathrans unaligned (and within reach of the syndicate for their plots).
Mission 3 will lead to the infiltration of Navras’ cell to finally arrest them and bring them to trial. The players will need to set up plausible cover, feign participation in Navras’ crimes to earn their trust and finally set up a trap and/or fight Navras henchmen.
You can even think of a fourth mission, revolving around several abducted persons, Navras has “stored” in a safe place as their “insurance”. In order to protect the innocent, Navras has to be set free within 24 hours – unless they are found prior to that time.