"genuine suggestions" is correct and usable in written English.
You can use it to refer to constructive, sincere, and honest advice. For example, "I asked my supervisor for genuine suggestions on how to improve my work."
Despite the chortles of his fellow councillors, Temple assured Guardian Australia it was a genuine suggestion.
However, Aintitcool's correspondent does report that the performances of Moretz and Smit-McPhee are rather good, with a genuine suggestion of eerie innocence to their relationship.
If only his successors as home secretary had bothered to consult with and listen to those who had genuine concerns and suggestions to offer about how an effective national offender management system might be developed, the hideous amount of time and money, wasted on unnecessary additional bureaucracy could have been spent on protecting the public by improving what was done with and for offenders.
[An ad campaign developed for UN Women, reveals how pervasive discrimination against women is through the use of genuine Google search suggestions.
Teachers respond positively and enthusiastically to praise, constructive suggestions and genuine attempts to improve their performance, as do professionals in other fields.
Whether or not the suggestion was genuine, Liverpool realised they could not afford to miss out on their No 1 target following experiences in previous windows where players have moved to other clubs while they refused to meet what they perceived as inflated demands.
One way of assessing Hume's position on this issue is to begin with Hume's suggestion that "genuine theism" involves the minimal claim that there exists some (invisible) "supreme intelligence" that is the origin, creator and governor of this world (NHR, 4.2).
Intuitively, Leibniz's suggestion is that genuine motion requires, in addition to relative change of place, a cause of that relative change.
