Well, he married Queen Amalia in 1836, meaning that their children would be born c.1840. Otto was having affairs by 1845/6, so that gives a decade of potential brood-rearing, although the number of children would be limited, even without physical issues (OTL Amalia didn't possess a uterus due to Mullerian agenesis), by their mutual distaste.
So if an heir is born in the early 40s, then that would lead to a wave of patriotism and more trust in the absolute monarchy. The downfall of the Bavarian politicos in 1843 would be delayed and Queen Amalia's position would be strengthened. She seems to have been rather outspoken and politically engaged, which made her unpopular, but her fertility might improve her public image.
What would probably happen is a similar Revolution to that of 1843, except in 1848, which would obviously make everything very apocalyptic, etc. Otto gave in to the Greeks in 1843 despite his wife's vocal opposition, so he is likely to do the same in 1848, and even if he doesn't, he will be defeated by the Athenian mob. By this time the money was running out and the Wittelsbachs were losing their enthusiasm for the Hellenic adventure, so Otto is in the same position as OTL, or worse.
Thus, Otto is either deposed in 1848 and replaced with his minor heir (unlikely because the hated Amalia would want to be Regent and because Otto II wouldn't have close relationships to the major powers - just look up the referendum on Otto's 1863 replacement to see how much of a priority this was - and because a minority rule would be seen as unstable) or by his younger brother (equally unlikely, for obvious reasons) or by a completely different candidate; or he struggles on as OTL to the 60s. Otto might not be deposed in 1862 if he has a son, and even if he is, that son will probably be enthroned by the revolutionaries. Otto dies anyway in 1867. After that, everything depends on the character of Otto junior and his family.
I don't know how the Greek role in the Crimean War would be affected, if at all, by this POD.