My own personal proposal, and one which would probably have the latest realistic POD, would be an ATL in which the Sikh Empire endures to the present day. This could be achieved in several ways, but the TL which I've put the most research into is one in which Nau Nihal Singh, Maharajah Ranjit Singh's grandson, manages to escape being knocked unconscious by falling masonry upon his return from his father's cremation, and evades assassination.
The Dogras' role in slowly poisoning his father Maharajah Kharak Singh to death, and attempting to bring about the miscarriage of his unborn son by the same means, is soon exposed, and the Dogras flee back to their power base in Jammu and Kashmir, igniting a brief civil war in the Sikh Empire. The Dogras attempt to boost their numbers by declaring the rebirth of the Sikh Confederacy, enticing a few ambitious misldars, and a couple of Cis-Sutlej states, to join their cause. In spite of the Dogras also approaching the British for support though, the BEIC rightly see it as a lost cause, and choose to stay neutral in the conflict, leaning towards the Sikh Raj due to their reliance on free passage through the territories they hold in order to continue their ongoing Anglo-Afghan War.
Eventually, the Anglo-Sikh Wars do still happen ITTL, when the unresolved issue of the Sikh princely states' involvement in the civil war comes to a head; but with better leadership, greater experience, better equipment and more troops than IOTL, the Sikhs win the first Anglo-Sikh War relatively comfortably, with the BEIC electing to sacrifice the guilty Sikh princely states (presumedly temporarily, with the intention of conquering them back and governing them directly after the next Anglo-Sikh War) to be annexed by the Sikh Empire in the peace deal, rather than paying indemnities.
However, this decision soon backfires on them, shaking the faith of India's sovereigns in the value of being British protectorates, and prompting several leaders to attempt to renegotiate their treaties with the BEIC- or in the case of some states, to attempt to end their treaty with the BEIC entirely. Among these, Khairpur (then encompassing the entirety of Upper Sindh) would be the most noteworthy- its ruler, Mir 'Ali Murad, already greatly mistrusted the British, and as such, he would take the lead in declaring that the British had failed in their duty to provide protection, ending his agreement with the British and entering treaty negotiations with the Sikh Empire instead.
Understandably, this draws the ire of the BEIC, but as they begin to amass enough colonial troops near the border to wage their Second Anglo-Sikh War and winning, preparing them for the coming war by equipping them with the latest Pattern 1853 Enfield rifles, rumors begin to spread about the cartridges, sparking off a far more severe Indian Rebellion than IOTL- with extra kindling also provided by the far more vocal opposition of the Company among the Indian Aristocracy ITTL, enough to turn it into a true 1st Indian War of Independence.
In spite of the enmity between them and the British though, the rebels' decision to rally under the banner of Bahadur Shah II, and to restore the Mughal Empire, would be the deciding factor for the Sikhs. With the resurrection of the Mughals perceived to be a far greater evil than the British could ever be, the Sikh Empire decides to offer its full support to the British in the conflict, enabling the British to eventually succeed in reconquering the short-lived Second Mughal Empire. In return for their assistance, and to cover their own financial losses in the conflict, one of the BEIC's final actions would be to sell the territories of Lower Sindh (incl. Kutch) and Bahawalpur to the Sikhs for a reasonable fee (with the Sikhs having to conquer these regions from the hostile occupying Mughal/Rebel forces themselves first).
After the formation of the British Raj, the military cooperation of the Sikh Empire with the British would lead to the signing of a formal military alliance between the Sikh Empire and the newly formed British Raj- with the Afghans' decision to become a protectorate of the Russians while the British were otherwise occupied reconquering Northern and Central India providing added incentive. As with OTL's Anglo-Japanese Alliance, while the British see as a warning to Russia, the Sikh Empire would be emboldened by it, seeing it as an open invitation for imperial expansion. Wakhan, the Baluch Kingdoms and the Sultanates of Oman and Zanzibar, along with large swathes of the Zanj Coast, would be their first targets- the Mahra Sultanate and Yakub Beg's Kashgaria would soon follow, and by the 1880s, the Sikhs set their sights on acquiring colonial territories, and establishing colonial settlements, further afield...