It is quite easy to prove that if $p(\theta)$ is a conjugate prior to some likelihood then the following:
$$q(\theta') \propto p(\theta)I(\theta \in A)$$
where $A$ is a subset of the parameter space and $I(r)$ is 1 if $r$ is true and 0 otherwise -- is also a conjugate prior.
Basically, if we take a conjugate prior and re-normalize it to a subset of the parameter space, we still get a conjugate prior family.
Is this mentioned somewhere that I can refer to?