Are Buddhists happier people?
The Buddha taught that doing wholesome and meritourious deeds will bring wholesome results.
Only wholesome actions can bring wholesome future resultants. That is a universal law, that can be verified by practicing insight meditation.
The Noble Eightfold Path teaches both morality and wisdom, e.g. Right Intention (Samma Sankappa), which is the opposite of the 3 unwholesome roots, namely Renunciation, Good-will and Harmlessness.
When a person does good deeds, observes ethical conduct (the precepts) and practices meditation in order to become free from suffering, then naturally that person will also become more happy, peaceful and less burdened by conditioned existence.
Why is that? Because ignorance (avijja) is what keeps a being chained to conditioned existence. Ignorance makes one believe that conditioned existence is happy, pleasant, controllable and enjoyable. Ignorance conceals the underlying impermanent, unsatisfactory and ungovernable nature of conditioned phenomena. When ignorance is present, one is increasing suffering for oneself1.
When one observes good ethical conduct and practices insight meditation correctly and consistently, then one will naturally develop wisdom, thereby slowly doing away with ignorance. The less ignorance the more happiness, roughly speaking.
Its also important to mention that one does not have to be a Buddhist to do wholesome deeds or to be happy. The word "Buddhism" is just conventional language meaning nothing in ultimate reality. We could call it any other word and it would not change anything.
Would it be fair to claim that Buddhists, if they practice well, can expect to be more content and generally more happy in their lives?
If one practices correctly and consistently, then one will not expect anything, because one has seen for oneself how expectation creates suffering and bondage.
Expectation is a hindrance and produces suffering. Expectation should be observed and noted, with mindfulness in the present moment, thereby using the hindrance to cultivate insight.
1For a detailed exposition on the process, see the doctrine of Dependent Origination (paticcasammupada).