Michael Barr calls 1290-1396 and 1511-1699 Singapore's first and second periods of prosperity.
Are there any estimates of Singapore's population during these two periods? (Even rough orders of magnitude would be helpful.)
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McEvedy and Jones's Atlas of World Population History (no longer in print, but if you can find a copy, buy it) has a separate call-out for the population of "Malaysia and Singapore". Obviously, that's not Singapore alone, but it could certainly be used as a ceiling.
It shows that entire area having about 300,000 souls around 1300, and steadily climbing up to about 600,000 by 1700.
A report from a Chinese traveler in 1330 was that there were two settlements on the island, so it wasn't a unified urban unit at the time. If you can find a version of his writings in a language you can read, its possible he might have provided a better idea of the rough size of those settlements.