Here's something I've come up with, A Longer Tudor Dynasty... in Ruler Game form!
The Tudor Dynasty (1485 - 1701)
The Direct Line
Henry VII [1]
Henry VIII [2]
Mary [3]
Jasper I [4]
Henry IX [5]
Jasper II [6]
Henry X [7]
Helen [8]
[1] Henry VII (Reign: 1485 - 1509) Divergence occurs in 1503 when Katherine Tudor was born with a male twin that was named Jasper, after Henry's uncle. Unlike Katherine and their mother Elizabeth of York, Jasper survived infancy and was granted the Duchy of York. Henry VII died as per RL due to tuberculosis and grief.
[2] Henry VIII (Reign: 1509 - 1530), the figure he very much was in RL, his wife Catherine of Aragon only managed to produce a single living child, the then Princess Mary. As a result, Henry VIII sought an annulment of his marriage based on Catherine's prior (unconsummated) marriage to Arthur, Prince of Wales so he could marry a courtier. However the proceedings became protracted as in RL due to the Pope being captured by Catherine's uncle, the Holy Roman Emperor, and then became irrelevant when in 1530 during a joust Henry VIII was killed by a stray lance through his throat due to his gorget coming loose.
[3] Mary of England (Reign: 1530 - 1533), the first uncontested female ruler of England found herself saved from potentially losing everything to becoming a Queen at age 14, she was swiftly wedded to her uncle (and heir), Prince Jasper, Duke of York. Their marriage was a happy one, though during Mary's regency (under the guidance of Queen-dowager Catherine and a Regency Council) the Kingdom had to contend with the attempts of the Protestant movement to gain a foothold in the land. The regency was ended upon Mary's 17th birthday (near the time when Jasper turned 16 and was trusted to 'help' Mary rule). Mary's reign was cut tragically short when she died miscarrying a stillborn son in 1533.
[4] Jasper I, (Reign: 1533 - 1557) a man whom few had anticipated becoming King, much less himself. At age sixteen he found himself on the throne, in his life he would marry three times (including Mary of England) and have a total of seven children (five of whom lived to adulthood). During his reign the foundations for what would become the Absolutist Period of English history would be lain. To counter-act the growth of the Protestant movement in England among the merchant and urban classes, Jasper experimented with a number of measures that would influence the Catholic Reformation, while militarily Jasper stayed out of the wars of religion that were affecting Europe, he did play a large role behind the scenes, offering loans, military equipment, and English mercenaries. Jasper died in his sleep at age 54.
[5] Henry IX, (Reign: 1557 - 1581) the eldest son of Jasper I, Henry IX is sometimes called 'the Unlucky' due to a number of crises that occurred during his reign. While the Protestants had been subdued by his father's measures, they weren't completely gone. A handful had traveled to Ireland and a movement that had quietly grown would erupt two years later that would ultimately reshape global politics, they would be known as the 'Purifiers', an extremist version of Calvinism that would come to dominate Ireland, the First Purifier Revolt would rock Ireland and England and was ultimately put due by ruthless measures implemented by Prince Arthur, Duke of York, more commonly called 'Bloody Arthur'. Not to mention a diplomatic backstab by France saw Calais fall in a sudden invasion and saw the end of England's last holdings on continental Europe. Meanwhile the sudden and mysterious death of Mary of Scots saw her illegitimate, Protestant half-brother James Stewart become James VII of Scotland and Scotland fall into a brief civil war that resulted in James's victory despite Henry's attempts at intervention for the remaining Catholic holdouts. During his reign infamous privateers and slavers like Francis Drake would unwittingly inspire the creation of the Southern Seas Trading Company (that helped shape the rise of Capitalism, for better AND worse. Henry unexpectedly died during an outbreak of fever in the spring of 1581 at age 46.
[6] Jasper II, (Reign: 1581 - 1601), the eldest son of Henry IX, it was in Jasper's reign that England truly began to flourish as a trading state despite the upheavals consuming Europe in general. It was the matter of Ireland that would dominate much of Jasper's time as the Purifiers (and their various branches) continued to inspire mutinies and minor revolts in Ireland, culminating in the Second Purifier Revolt that was put down after four years of savage fighting that saw Dublin burned down to the ground. This inspired many Irish (both Catholic and Purifier) to head to the New World, even while Jasper and several other monarchs established official colonies as the Spanish 'monopoly' on the region completely broke down. Jasper II was assassinated by an Irish Purifier during a royal progress in 1601.
[7] Henry X, (Reign: 1601 - 1663), the only surviving son of Jasper II, Henry X of England came to the throne at age 10 in 1601, his early reign was dominated by William Laud, Archbishop of Canterbury who ruled as Regent and was an important advisor to the King until his own death. It was during Henry's reign that the 'Absolutist Period' of English History is considered to have begun. With Laud serving as the prototype for the future 'First Ministers of the Crown', Henry was able to effectively delegate important positions and jobs in government and the court while maintaining control over most operations. In the 'Eternal Game' of the era (balancing Spain and France against each other), Henry was able to keep both nations from gaining too much power by always undercutting them when it was needed, helping the weaker one, but always shying from a direct confrontation. It is believed that he engineered the coup that saw Henri IV 'the Protestant' overthrown when he reneged on his Catholism and tried to make France a Huguenot state and saw the rise of César I of France (Henri's illegitimate son who had been raised Catholic) to the French throne. While Henry X had had four sons with his first wife, Queen Maria Anna of Austria, late in his life they had all died and among them was only a single, living child among them, his granddaughter, Princess Helen, Duchess of Somerset. Henry spent some time in teaching her to rule, all the while trying to sire a new son with his brief second wife, Queen Louise of Anjou (she only bore him a daughter named Catherine). Henry died of small pox at age 69.
[8] Helen, (Reign: 1663 - 1701), the only surviving grandchild of Henry X, Helen of England came to the throne three days shy of her 18th birthday, there was some discussion of a regency but Helen requested that it be waived in favor of her marrying as quickly as possible. Despite being considered 'plain', Helen had many suitors but ultimately married Louis Fitztudor, Duke of Monmouth (a descendant of a bastard of Jasper I). More interested in culture, music, and other arts, Helen largely left government business in the hands of her husband and his ministers (the 'Monmouth Set') and focused on things that were more suited to a Queen-consort than a ruler. However she didn't completely abdicate control and from time to time made her views and opinion's known (and usually got her way). Helen would have a total of six children and a single stillbirth that left her depressed the rest of her life. The death of Louis Fitztudor in 1680 caused Helen to withdraw almost completely from public life, leaving the nation effectively in the hands of her son, Prince Henry who ruled as a regent in all but name. Helen died of natural causes in 1701, ending the direct line of the House of Tudor, though her children would take up the name they are often called the 'House of Tudor-Monmouth' as a distinguisher.