I've added 咳が出る.

咳	1,476,178		
咳が	483,506		
咳を	165,641		
咳が出	78,472		
咳をする	36,703		
咳をし	81,483

I don't think a note is appropriate here. 咳が出る is probably worth having as an entry.

@@ -21 +20,0 @@
-<s_inf>often as 〜が出る or 〜をする</s_inf>

It's a good point about 咳をする and 咳が出る; the EJs give them as Japanese glosses for "to cough". It might be worth including one or both.

@@ -21 +21 @@
-<s_inf>〜が出る, 〜をする</s_inf>
+<s_inf>often as 〜が出る or 〜をする</s_inf>

咳をする	36703	35.2%
咳が出る	49006	46.9%

咳をした	7339	7.0%
咳が出た	2550	2.4%

咳した	1085	1.0%
咳く	581	0.6%
咳いた	142	0.1%
咳出た	84	0.1%
こほんこほん	424	0.4%
ゴホンゴホン	5285	5.1%
コホンコホン	1182	1.1%

I'm marking 咳く as [rare] and pointing it here for lack of anywhere else to point it.

How to handle? JMDictdb has one verb form for "to cough" 咳く, and it is particularly rare.  咳 is not [vs], but it is をする, and just as often が出る (the form I learned in school).  "to cough" seems like a pretty unfortunate omission. (コホンコホン would do in a pinch, if someone is studying their onomatopoeia). 

I'd probably create both 咳をする　and 咳が出る as independent entries, but I'm too afraid they'd be immediately rejected.  There is a "danger", if slippery-slopes are of concern, that there are other medical terms that work this way.  I think 血が出る is "to bleed" (which is also missing), although 鼻血が出る (to have a nosebleed) is already here.  I think "to cough" would be a worthy exception if this was considered exceptional.

I also don't mind just handling as a note like I've done. (also, even as an exception).

I checked on bleeding...
血が出る	49473
鼻血が出る	19806
出血する	48773

@@ -20,0 +21 @@
+<s_inf>〜が出る, 〜をする</s_inf>