With added sugars, the answer seems obvious: Zero added sugar is best, but maximum is 25 grams for women, and 37.5 grams for men. (source)
That source is referencing the American Heart Association, in which they estimate that half of the 'discretionary calories' recommended by the (now superseded) 2005 US Dietary Guidelines1 could safely come from added sugar. These discretionary calories vary greatly with total daily calorie intake, and the difference values given by the AHA are based on further assumptions that men eat 2200 kcal/day and women eat 1800 kcal/day.
These value are absolutely not applicable for athletes, who are likely eating far more than 2200 kcal/day. For instance, the 2005 US Dietary Guidelines allocate 648 kcal of discretionary calories for people eating 3200 kcal/day, and half that amount would be 81 grams of sugar.
However, with the natural sugars, the answer is unclear. From this source, it lists multiple recommended serving sizes for fruit, vegetables and dairy.
That source is terrible for multiple reasons, and you should probably just ignore everything it says. It wrongly divides sugars into 'natural' and 'added', which results in the absurd claim that honey and agave nectar are not forms of added sugar, despite being almost pure sugar. It claims that natural sugars are only made from fructose and lactose, but in reality all fruits contain a mixture of varying amounts of fructose, glucose and sucrose.2 It states that one teaspoon of added sugar has 15 calories and excessive intake can lead to weight gain and obesity, but neglects to mention that the exact same holds for sugars naturally present in whole foods.
The real answer is that all sugar is natural, and 'natural' vs 'added' sugar is not a useful distinction, but 'whole foods' vs 'added sugar' is useful. The distinction between the two is that whole-foods contain other nutrients of benefit, and it is much harder to overeat on whole-foods than it is on, say, sugar sweetened beverages. However in this categorisation, any concentrated form of sugar must be considered 'added' sugar, regardless of to what degree it is processed. This includes all forms of sugar, honey, and agave nectar. Dried fruits, due to the fact they they concentrate the sugar content of the fruit, could also be considered 'added' sugar.
Within this categorisation, which is much more in line with the intentions of the American Heart Association and US Dietary Guidelines, you could stick to a limit of half the current guidelines'3 discretionary calories intake coming from added sugar, and not worry about limiting sugar from whole-foods at all, as long as your total calorie intake is not excessive.