You can butterfly away the OTL mass-migration of Turkish tribes into central Anatolia plus areas of the South and North quite close to the coasts, in the 1070s - which was never reversed even at the height of the Comnene recovery in the mid-C12th - by a few major changes to Byzantine politics and military events in the 1050s to 1070s. Most plausibly, have a series of stable and decently competent 'legitimate' emperors following Basil II who keep a grip on the court nobility and bureaucrats, prioritise the army and tax-raising, and do not alienate the provincial aristocratic elites to the extent that there is a series of rebellions (eg 1043 by Maniaces, 1047 by Leo Tornicius, and 1057 by Isaac Comnenus and his allies in OTL). If Basil II is temperamentally unwilling to marry, have him insist on his weak brother and heir Constantine VIII marrying off his eldest daughter (either Eudocia, who ends up in a convent after having smallpox, or his OTL successor Zoe) to a capable general who continues Basil's policies after C dies in 1028. Otherwise , either military strongman Maniaces wins his revolt against Zoe and her easygoing and over-cautious civilian husband no. 3, Constantine IX, in 1043 and revives a strong and flexible army or Isaac Comnenus has much longer for his military reforms after 1057 and passes the throne in the later 1060s or 1070s to his nephews (Manuel if he is not killed as in OTL, or the actual ruler from 1081, Alexius I) and one of this trio wins the battle of Manzikert.
A competent Byz emperor/ general who has full support and no plotters ready to stage a coup behind his back (as Romanus IV did in 1071 in OTL) and an adequately trained and flexible army with cavalry archers (Pecheneg or mercenary non-Saljuk Turks?) to keep the Saljuks from over-running the defensive Byz infantry phalanxes at Manzikert, plus no panic, muddle or treason at the battle as in real life, would at least secure a draw and keep the army intact. This luck/ skill plus some stronger Byz defensive units to patrol the frontier and catch raiders. logically settled in the region so incentivised to defend their own homes, would hopefully check the Turks. The latter usually preferred 'hit and run' tactics on swift cavalry raids and looting from unarmed civilian farmers and unwalled towns to a pitched battle, so would they give up attacking Anatolia after a mauling in a major battle and head for Syria instead to loot and settle there? The Saljuk Sultans, as 'protectors' of and strongmen behind the Sunni Caliphs in Baghdad and in only precarious command of their tribal vassals ( a factor often forgotten by historians - the 1060s Turkish raids in to Anatolia were by tribal opportunists not by the Sultan's orders), would also have the incentive of driving the unwelcome 'heretic' Shi'a Fatimids out of Syria/ Palestine, plus a lack of major Sunni states in Syria capable of holding them back. That way, we get a major Turkish nomad migration to Syria and Palestine not to Anatolia in the 1070s to 1090s, and if a line of competent Byz rulers with a large and viable army with adequate cavalry continues - aided by more Western knights lured to join up by Alexius with a promise of lands on the frontier? - things stay that way. If the Turks settle in Syria in large numbers, we also get butterflies for the Crusaders if they arrive as in OTL 1098 to 'rescue' Jerusalem- more Moslem enemies intent on attacking them and a greater chance of failure, or at least of having to rely on Byz help and admit Alexius as their overlord. A mass of quarrelsome rival Turkish warlords in Syria ruling mini-kingdoms also provides headaches for any would-be unifier, eg Zengi, Nureddin, and Saladin.
The lack of a large or militarily coherent civilian local population or many large walled cities in sparsely-populated and infertile upland eastern and inland central Anatolia is a continuing Byz problem - so if the frontier is breached and/or the army defeated , or a civil war in the capital distracts the military, there is no 'defence in depth' and it is open season for invaders. But a 'defence line' of smallish fortresses and blocked passes plus mobile army units across the East of Anatolia, probably SW (Cilicia) via the Theodosiopolis/ Erzerum area to the NE (at the Black Sea's SE corner, near Phasis) is easier to hold for Alexius I , his hugely capable son John II, and John's showy and risk-taking but reasonably flexible son Manuel I , in c. 1080 to 1180 than the 'bow-shaped' OTL frontier, which had the Turks still occupying central Anatolia (one, Saljuk state at Konya, a smaller , Danishmend state to the N, and assorted roaming tribes), and all 3 emperors were capable of keeping the army in action year by year to keep up training and ward off raiders. In this scenario, if - a big 'If' but plausible - stability in Constantinople continues under a longer-lived Manuel (d aged around 62 in 1180 in OTL) , who lasts until his half-Crusader son Alexius II (born 1169, son of a princess of Crusader Antioch) is adult and a Byz-Crusader alliance keeps going and holds Saladin back, we get no Myriocephalum battle disaster in 1176, no tyranny of Andronicus I in 1183-5 fracturing the Byz elite, no disastrous Angeli dynasty, no 1204, and no Horns of Hattin Crusader disaster of a Byz-led rescue of Jerusalem in 1187-91. Do we have Alexius II and his army rescuing his mother's city, Antioch, and then the Kingdom of Jerusalem as 'leader' of the Third Crusade if Saladin takes J, and so improving Byz-Western relations but annoying his own elite by 'wasting' resources on ' barbarian Latins' and 'heretics'? That way, I can see a continuing and centralised Comnene dynasty (if Alexius II dies without a son or is overthrown as 'too Latin and pro-heretic', perhaps led by Andronicus I's capable grandsons Alexius and David, OTL founders of the Trebizond dynasty), or even Theodore Lascaris and John III Vatatzes keeping the Byz state ruling most or all of Anatolia until the Mongols arrive. (There is also a militarily useful new population of exiled Armenian refugees from the Saljuks in SE Anatolia to defend that area, though they are not Orthodox Chalcedonian Christians so the Byz Church could cause persecution and anti-Byz revolts.)
The chances of the Empire keeping hold of Anatolia in and after the 1240s and not suffering a Kose Dagh-style defeat by the huge Mongol army in 1243, as the Saljuks did in OTL, must be limited - and an equivalent of Manzikert then and a huge flood of Mongols and Turcoman nomads into central Anatolia as a result are likely. John Vatatzes if anyone is capable of holding onto the West and stabilising a frontier line (across the centre of the peninsula from Attaleia N via Dorylaion to Sinope and Trebizond?) with resettled Christian refugees plus a rebuilt army, logically with the OTL Empire of Nicaea military/ civilian 'theme system' admin structure plus his tax-raising priorities saving the Empire. This frontier could stabilise for centuries if the Byz stay united (not too hopeful but possible given a line of adult and sane father to adult and sane son descent of the throne as with the Capetians in France). But holding the far East of Anatolia too would really depend on the Mongols heading in another direction in 1243 , given their vast resources that the medium-sized Comnene Byz state could not match - perhaps there's a Mongol decision to 'chase ' the refugee Khwarizmian Turk nomad coalition (driven out of Iraq by the Mongols) across Syria to Palestine in 1243-4 instead, and/or the Saljuks - ruling in Syria , probably at Aleppo, in this timeline - distract the Mongols into a war. if this war and the Mongol campaigns of 1258-60 are all safely beyond the Byz frontier in the Fertile Crescent, I can see a Byz state plus a larger Cilician Armenia lasting for centuries - but at some point the mass of Turcoman tribes roaming around the Kurdistan / Azerbaijan areas are likely to be turned by a charismatic leader into a 'jihad' against the Christians. A lot will depend on a stable and large-size Byzantium taking on the OTL role of the Ottoman state and not being stabbed in the back by Western land-hunting kings like Charles of Anjou...