“a suggestion on doing sth”这个搭配有么？

有的，比如：Can you give me any suggestion on this matter?

suggestion是名词he made some helpful suggestions but her boss regected them all.
可以用suggestion on/for/about sth
e.g. we welcome any comments and suggestions on these proposals.
对于这些方案的任何评论和建议，我们都欢迎。

动词形式是：suggest
有suggest sth (to sb) a solution suggested itself to me.
suggest (that) i suggest that we go out to eat.我建议我们出去吃。

a suggestiong of doing sth.

上面两者似乎都对