I have tried to make a list of all the rulers of Bombay. I'm in no way an expert, but did my best.
Some coins look like to be minted under the British rather than the Mughal emperors, so made a list of the relevandt British monarchs on the bottom, but maybe some of them are more appropriate for the East India Comapny? Blurry lines between the Crown and the Company..?
There seems to have been a couple of brothers who had the defacto power from 1712 to 1748, who I think can be an alternative in that ruler period.
Mughal Empire: Bombay Presidency
Timurid dynasty - House of Babur
- Aurangzeb/Alamgir (1658-1707)
Wiki: Q485547
Example: N#355385
- Farrukh Siyar (1713-1719)
Wiki: Q559490
Example: N#79768
- Muhammad Shah (1719-1748)
Wiki:Q558714
Eksample: N#58337
- Ahmad Shah Bahadur (1748-1754)
Wiki: Q400807
Example: N#67699
- Alamgir II (1754-1759)
Wiki: Q732026
Example: N#91910
- Shah Jahan III (1759-1760)
Wiki: Q2627138
Example:
- Shah Alam II (1760-1788 & 1788-1806)
Wiki: Q719449
Example: N#77713
Dynasty: Timurid dynasty - House of Babur - Puppet of the East India Company
- Akbar Shah II (1806-1837)
Wiki: Q2091579
Example: N#89524
Dynasty: Timurid dynasty - House of Babur
- Bahadur Shah II Zafar (1837-1857)
Wiki: Q127369
Example: N#73909
From 1712 to 1748 alternatively:
- Sayyid brothers (1712-1722)
Wiki: Q7429370
Example:
British Empire - House of Hannover:
- George I (1714-1727)
Wiki: Q130805
Example: N#25882
- George II (1727-1760)
Wiki: Q131981
Example: N#25882
- George III (1760-1820)
Wiki:Q127318
Example: N#50015
- George IV (1820-1830)
Wiki: Q130586
Example: N#75740
- William IV (1830-1837)
Wiki: Q130822
- Victoria (1837-1901)
Wiki: Q9439
Example: N#219955
Referee @SStefanov will maybe give an opinion? :D
Sources:
https://en.wikipedia.org/wiki/List_of_emperors_of_the_Mughal_Empire