Some children of Konstantinos X, both those born earlier & porphyrogennetoi, became co-emperors

Summary:
When Konstantinos X ascended the throne he was followed to the palace by his daughters and three sons, Michael (VII), Andronikos and another, who died soon after his accession. Before a year of his reign had passed Konstantios was born, and as porphyrogennetos was immediately given the title of emperor. Shortly after Konstantinos adorned Michael (VII) too with the imperial diadem, testing him as he was about to take the throne to see if he was fit to be emperor by asking about the separation of political principles. Michael gave his question a valid answer. Konstantinos took this as an omen that he was destined to be a distinguished emperor, and at once completed the ceremony of enthronement. Andronikos was crowned soon after 
Dates:
1060 
Andronikos Doukas, brother of Michael VII (Andronikos 62)
second son of Konstantinos X and Eudokia (Anonymus 7035)
  • He lived for a short time after Konstantinos 10's accesion, then died μετὰ τὴν ἀρχὴν ὀλίγον ἐπιβιοὺς ἀποθνῄσκει Psellos: Chronographia VIIa 20.7-8
Emperor Konstantinos X Doukas (Konstantinos 10)
  • When he ascended the throne he was followed to the palace by his children (Michael 7) and made them co-emperors, while those born after his accession in the purple chamber were also made co-emperors (Konstantios 61) (:) καὶ τῇ πορφυρίδι κατὰ τὸν τῶν Ῥωμαίων ἐθισμὸν συναναδοθέντων Attaleiates: History 77.23-78.4 / 59.9-12
  • Proclaimed emperors his three sons Michael 7, Andronikos 62 and Konstantios 61 who was the only porphyrogennetos, and appointed his brother (Ioannes 62) kaisar, making him an accomplice in his plans (:) Skylitzes Continuatus 118.7-10
  • Before a year of his reign had passed Konstantios 61 was born to him and he was immediately dignified with the name of emperor (:) ὁμοῦ δὲ τίκτεται παιδίον τῷ βασιλεῖ, καὶ τοῦ βασιλείου εὐθὺς καταξιοῦται ὀνόματος Psellos: Chronographia VIIa 21.1-3
  • Shortly after (the birth of Konstantios 61) he adorned Michael 7 with the imperial diadem, testing him as he was about to take the throne to see if he was fit to be emperor by asking about the separation of political principles (:) δοκιμάζει γενναίως εἰ προσήκων τῇ βασιλείᾳ γένοιτο Psellos: Chronographia VIIa 21.6-11
  • Michael 7 solved his question and gave a lawful answer; he took this as an omen of a spirit destined to be distinguished as emperor and at once completed the ceremony of enthronement (:) αὐτίκα τούτῳ τὴν βασίλειον πανήγυριν ἐκτελεῖ Psellos: Chronographia VIIa 21.11-14
  • Adorned Konstantios 61 with imperial insignia immediately and before his other sons (Michael 7 and Andronikos 62), because Konstantios 61 was born in the purple; then he also proclaimed the others (Michael 7 and Andronikos 62) (:) Zonaras 18.9.20
Konstantios Doukas, brother of Michael VII (Konstantios 61)
  • Because he was born in the purple, Konstantinos 10 adorned him with imperial insignia immediately and before his other sons (Michael 7 and Andronikos 62) (:) Zonaras 18.9.20
  • He was born before a year of Konstantinos 10's reign had passed and was immediately dignified with the name of emperor (:) ὁμοῦ δὲ τίκτεται παιδίον τῷ βασιλεῖ, καὶ τοῦ βασιλείου εὐθὺς καταξιοῦται ὀνόματος Psellos: Chronographia VIIa 21.1-3
Emperor Michael VII Doukas (Michael 7)
  • Shortly after (the birth of Konstantios 61) Konstantinos 10 gave him an imperial coronation, testing him as he was about to take the throne to see if he was fit to be emperor by asking about the separation of political principles (:) δοκιμάζει γενναίως εἰ προσήκων τῇ βασιλείᾳ γένοιτο Psellos: Chronographia VIIa 21.6-11
  • He solved the question and gave a valid answer; Konstantinos 10 took this as an omen of a spirit destined to be distinguished as emperor and at once completed the ceremony of enthronement (:) ὁ δὲ διαγινώσκει τὸ ζήτημα καὶ ἔννομον ποιεῖται ἀπόφασιν Psellos: Chronographia VIIa 21.11-14
  • Konstantinos 10 adorned Konstantios 61 with imperial insignia immediately and before his other sons (Michael 7 and Andronikos 62), because Konstantios 61 was born in the purple; then he also proclaimed the others (Michael 7 and Andronikos 62): in association with Andronikos 62 (:) Zonaras 18.9.20