Alexander III did attempt to establish a Duma but was assassinated before the plan was publicized.
We never got to see this Duma in action, and aside from merely confiding that he planned it, Alexander II never made any significant steps to bring it into existence during his tenure as Tsar. He made a
tiny concession of power on his deathbed that would have limited the Tsar's authority relative to his advisors but this was signed out of existence by his successor upon his coronation.
Alexander II was less a liberal tsar and more a pragmatic autocrat who sought to keep the Russian monarchy in place by making concessions he felt were necessary to keep stability. His rationale for emancipating the serfs amounted to "Either we free them ourselves, or they'll free themselves at the end of a bayonet", while it could be argued that he was saying this to assuage his conservative opponents, it probably says more about precisely how "liberal" the Tsar Liberator actually was.
That and the radicals earnest attempts to assassinate him were what drove him from the reformist platform as he became disilluioned with the whole process.
Now if Alexander II had not been assassinated Alexander III may have been slightly less on the repressive side and may have seen the benefit of further reform and a loosening of restrictions.
Alexander III was already pretty socially conservative (this owed to a deliberate consequence of his upbringing and mentorship), and deeply resented his father for, among other things, having a mistress.
It does bear mentioning that Alexander III did actually enact a very good deal of reforms, what causes his reforms to be forgotten is the fact that he coupled the changes he did make to Russia's economy and administration with a very severe campaign of repression and the promotion of conservative causes (namely Orthodoxy and Russian cultural superiority). He abolished the poll tax on the Russian peasantry and created a viable institution to provide credit to the Russian peasants and through this was basically able to reverse the disastrous aftereffects of the abolition of Russian serfdom (which, like the aftermath of slavery in the United States, relapsed into horrendous economic conditions in which former slaves wound up deeply indebted to their former masters), not to mention giving the Russian Empire a major kick forward on industrialization.
If I had to pick a single title to describe Alexander III, it would probably be something along the lines of efficient autocrat: his methods were
not at all liberal or very pleasant, but he was utterly convinced of himself and turned out to have some very good ideas about how to fix the Russian system.