I'm more comfortable discussing efforts other than force that were used to maintain order than I am in assessing Iraq's stability as I think that's a bit of a political and counter-factual mine field.

Saddam's Iraq was basically a patronage state in which money and appointments flowed from Saddam to favored groups and cronies in a complex web of financial and official favoritism. Some of this was based on personal relationships (e.g. Saddam's own family), some to favored groups (e.g. Sunnis and certain other minority groups including, as I understand it, Assyrian Christians edit: see /u/550-Senta 's comment below about Chaldean Catholics and Assyrians) and some were massive all-encompassing state programs and bureaucracies that while they institutionally favored these groups were nonetheless enormous (e.g. the army, the oil ministry and so on).

Use of a massive conscript army to foster national unity was not just a form of patronage but also an attempt to form national identity and is an effort that carries over dating to the formation of Iraq in the 1920s and is in many ways characteristic of 20th century Arab states generally where the same is largely true of, say, Egypt.

A national, Iraqi identity was also a key part of Iraqi propaganda efforts under Saddam, which often tried to portray, for example, the Iran-Iraq war in Arab-Persian terms rather than Sunni/Shia. Insofar as Saddam latched onto religious causes it was usually of a pan-Islamic variety, like antagonism to Israel. This changed with the "Faith Campaign" in the 90s which marked a turn towards Sunni Islamism but as I understand it this is both controversial and hotly debated, and it's not a topic I'm especially well-versed in.

While it might be considered as a form of "force" Saddam also maintained an extensive intelligence apparatus. The Iraqi intelligence services were enormous, and much like their counterparts in the soviet bloc or other dictatorial regimes their reputation mattered as much as their actual reach.

That was combined with a top-down institutional control so that, for instance, the government might not just control the leadership of labor unions, it would then spy on union meetings. This kind of approach was pervasive in Iraqi society, and the threat of extreme force was ever present.

While as I said I don't want to really make an assessment of stability, it is nonetheless clear that these efforts didn't really work in creating a solid Iraqi identity, or in keeping the disparate elements of Iraqi society in line. This was particularly true of Iraqi Kurdistan, which basically was given de-facto autonomous protection after 1991 as part of Operation Provide Comfort, but can also be seen in the Shia Uprisings in 1991 and 1999 which resulted in low-level violence and popular hatred of the regime by the majority-Shia population until the overthrow of the regime in 2003.

Edit: also, in addition to the above it would be worth highlighting things about the Saddam regime that, from the Iraqi perspective would have seemed like positive developments. For instance, Saddam cultivated Iraq's education system. Mosul Dam (even if it was terribly built) provided electric power for all of Mosul. The economy seemed to be doing well prior the Gulf War. I don't want to be misunderstood as saying that Iraqi standards of living were improving under Saddam more than they would have otherwise, but prior to the Gulf War they were nonetheless improving in a way that likely contributed to stability.

Source wise:

As far as I'm aware, the most comprehensive book on this to date is Charles Tripp's A History of Iraq.

Kyle Orton is an academic who has written some of the more interesting analyses of Saddam's Faith Campaign, but there's a definite current political aim to his work (i.e. that the roots of Islamic State and Iraqi Sunni extremism are in the Saddam regime, not the US invasion) and it has therefore been subject to debate. As I mentioned this is at the cutting edge of our 20 year rule and it's not a topic I'm well versed in. It's very much being played out in popular media (i.e. Here, and Here) with an eye towards recent events, so I think it would be prudent to wait for more formal academic analysis of the question in the coming years, particularly as, as far as I'm aware, we haven't even scratched the surface of dealing with the Iraqi primary sources.