"could be obliged" is correct and usable in written English.
You can use it to express that someone is willing to do something for a favor they have been given. For example: "He could be obliged to help them out with their project."
The county's public safety division, which operates ambulance services, says it could be obliged to cut staff.
While they could be obliged to do pro bono work at night instead of classes, fewer good options exist for those who have day jobs.
Assuming a presidential election is held in June, and that Mr Karzai wins, he could be obliged to rule by decree for almost a year.
If the Black Swan turns out to be a Spanish warship, Odyssey could be obliged to surrender its haul to Spain.
Just as euro-zone members are required to have an independent central bank, they could be obliged to set up independent offices of statistics and budget sustainability and to enact constitutional guarantees of good behaviour.
Public enterprises and private enterprises that receive tax dollars could be obliged to achieve economic diversity in hiring, which means they have to pay special attention to applicants whose families are in poverty or near poverty.
This suggested a way in which probable evidence, for example probable evidence for the existence of an afterlife, could be obliging on us and was crucial to his arguments for the reasonableness of basic Christian teachings in the Analogy.
They could also be obliged to hold a minimum level of capital to cover potential losses.
Accusation: Until now, journalists could only be obliged to reveal their information sources using criminal law procedures; from now on, the Media Council and the authority have the power to do this.
For several years, the homeowners' lawyers have sought to have HUD take control of the properties and return them to the original owners, who could then be obliged to make some back mortgage payments and pay taxes.
