Is there a symbol used with AD and BC to mean "possible date"?

I don't know whether historians use it in this way, but one of the many uses of the tilde (~) is "approximation".

Robinson discovered the island in ~202 BC.

would therefore be read/understood as

Robinson discovered the island in approximately 202 BC.

Circa:

(written abbreviation c); (ca)
(used especially with years) approximately:
He was born circa 1600.

The Oxford English Dictionary prepends the letter c to indicate an approximate year:

c1400 (▶?c1380) Pearl

a quotation from a manuscript of around (= circa) 1400 preserving a text probably composed around 1380. (The symbol ▶ preceding a date indicates that this is a date of composition, not a manuscript date.)

This is also used in the Middle English Dictionary, for example.

If historians are uncertain about the date, is there a simple and short notation they can add to the date, to indicate the uncertainty? I'm looking for something like this, but more professional:

Robinson discovered the island in 202 BC (?).

Yes, there is a symbol and it is (Ahem......) (?).
Your use of (?) is professional and correct.

According to Sussex University Website:

The question mark also has one minor use: it may be inserted into the middle of something, inside parentheses, to show that something is uncertain.
The question marks on the poet's birth and death dates indicate that those dates are not certain.

Summary of Question Marks:

• Use a question mark at the end of a direct question.
• Do not use a question mark at the end of an indirect question.
• Use an internal question mark to show that something is uncertain.

[University of Sussex]

Also from White Smoke:

Use a question mark enclosed in parenthesis (?) if a date or another number is unknown or doubtful among the experts. Do not use a question mark to communicate that you are unsure of the information you write, as this weakens the authority of your writing.
Joan of Arc, 1412 (?) – 1431, is considered a French heroine.

Also see Jozef Pelsudski Institute.

The tilda ' ~ ' is used to express an approximation:

Robinson discovered the island in ~202 BC. = Robinson discovered the island in approximately/about/ in some year close to 202 BC. (See https://en.wikipedia.org/wiki/Tilde)

The question mark is used to give a date which is, in the view of the writer, probably correct but over which there is some doubt.

Robinson discovered the island in 202 BC(?) = It is thought that the year was 202BC when Robinson discovered the island.

According to New Hart's rules: the handbook of style for writers and editors, Oxford University Press, 2005, p. 183, ISBN 978-0-19-861041-0, the multiplication sign (×) may be used when the exact date is unknown, but some bounds are established:

When referring to events known to have occurred between two dates, historians often employ a multiplication symbol 1225 × 1232 (or in some styles 1225 × 32) means 'no earlier than 1225 and no later than 1232'. The multiplication sign is also useful if one element of a range is itself a range: 1225 × 32 - 1278

Re the currently low-voted answers: I would caution that if you're going to use "(?)" to indicate uncertainty in formal written English, (A) don't, and (B) be very careful about its placement.

Robinson discovered the island in 202 BC(?).

Does the writer mean that Robinson definitely discovered the island, maybe in 202 BC? Or that it's uncertain whether Robinson was the discoverer at all? Or that the writer is certain that Robinson discovered the island in 202, but isn't sure if it was BC or AD?

Robinson discovered the island in 202(?) BC.

This version reads much clearer to me personally. The "(?)" is clearly attached to the date "202"; Robinson's discovery is not in question, and neither is the fact that the "202(?)" refers to a time BC. Compare to alternatives such as

Robinson(?) discovered the island in 202 BC.

Robinson discovered the island(?) in 202 BC.

However, if you mean something, it's almost always clearer to just say that thing in English, rather than trying to encode it in the placement of punctuation.

Robinson is thought to have discovered the island in 202 BC.

The island was discovered by Robinson; Friday gives the year of its discovery as 202 BC, but other historians have contested that timeline.