Very similarly to this, how do you stop letter labels being inserted after the years in citations of references with the same year (and author(s)) when using the agsm bibliography style? What changes need to be made to agsm.bst?
I suggest you proceed as follows:
Find the file
agsm.bstin your TeX distribution. Make a copy of this file and call the copy (say)
agsm-noextrayearlabels.bst. Do not modify an original, unrenamed file from the TeX distribution.
agsm-noextrayearlabels.bstin your favorite text editor; the program you use to edit your tex files will do fine.
Go to line 1301 in the file, where you should find the line
Comment out this line -- or delete it.
Save the file
agsm-noextrayearlabels.bsteither in the directory where your main tex file is located or in a local directory that's searched by BibTeX. If you choose the latter option, be sure to also update the filename database of your TeX ditribution.
In your main tex file, change the instruction
Rerun LaTeX, BibTeX, and LaTeX twice more to fully propagate all changes.