Shortstack in table entries

In an effort to achieve your desired result with minimum changes to your original code, I added one line and changed another. I first added the line usepackage[usestackEOL]{stackengine} to have access to the addstackgap macro. Then, I modified your header row of the tabular, so that one of the cramped stacks was enclosed in an addstackgap, such as multicolumn{1}{c}{addstackgap{textbf{shortstack{Paying\ members}}}}. This applies a 3pt vertical buffer around the object.

documentclass[12pt]{report}
        usepackage{tabulary}
        usepackage[maxfloats=30,morefloats=12]{morefloats}
        usepackage{booktabs}
        usepackage{float,lscape}
        usepackage{longtable}
       usepackage{pdflscape}
        usepackage{tabularx}
        usepackage{multirow}
        usepackage{bigstrut}
        usepackage[usestackEOL]{stackengine}
        begin{document}

begin{table}[htbp]
  centering
  caption{ETV 1830 - 1930}
  tiny
    begin{tabular}{rrrrrrrrr}
    hline
    multicolumn{1}{c}{textbf{Year}} & multicolumn{1}{c}{textbf{Organizations}} & multicolumn{1}{c}{textbf{Associations}} & multicolumn{1}{c}{addstackgap{textbf{shortstack{Paying\ members}}}} & multicolumn{1}{c}{textbf{in % of total}} & multicolumn{1}{c}{textbf{shortstack{Non-paying\ members}}} & multicolumn{1}{c}{textbf{in % of total}} & multicolumn{1}{c}{textbf{shortstack{Total\ members}}} & multicolumn{1}{c}{textbf{shortstack{Active\ members}}} bigstrut\
    hline
    1830  & -     & 2     & -     & -     & -     & -     & -     & - bigstrut[t]\
    31-40 & -     & 7     & -     & -     & -     & -     & -     & - \
   hline
    end{tabular}%
  label{tab:addlabel}%
end{table}%

end{document}

Furthermore, if you desired the header row top-aligned, you can change every instance of shortstack to Shortunderstack (note the capital leading "S"), to obtain:

You can have what you want in a simpler way: the makecell package allows for line breaks in cells, and a common formatting (incl. vertical alignment) in specific table cells, thanks to the thead and makecell commands. To have a better vertical spacing, simply use the booktabs package. Finally captionproduces a correct vertical spacing between caption and table when the former is above the table, and you can customise further the caption.

Thus it is possible to have a table in footnotesize except for the column heads which are in scriptsize – instead of tiny, which almost unreadable:

    documentclass[12pt]{report}
    usepackage{tabulary}
    usepackage[maxfloats=30,morefloats=12]{morefloats}
    usepackage{booktabs}
    usepackage{float,lscape}
    usepackage{longtable}
   usepackage{pdflscape}
    usepackage{tabularx}
    usepackage{multirow}
    usepackage{bigstrut}
    usepackage[showframe]{geometry}
    usepackage{caption, makecell, booktabs}
    captionsetup{font = footnotesize}
    renewcommandtheadfont{bfseriesscriptsize}
    renewcommandtheadalign{bc}

    begin{document}

    begin{table}[htbp]
      centeringsetlengthtabcolsep{3.5pt}
      caption{ETV 1830 - 1930}
      footnotesize
        begin{tabular}{rrrrrrrrr}
        toprule
        thead{Year} & thead{Organizations} & thead{Associations} & thead{Paying\ members} & thead{in %\ of total} & thead{Non-paying\ members} & thead{in %\ of total} & thead{Total\ members} & thead{shortstack{Active\ members}}\
        midrule
        1830 & -- & 2 & -- & -- & -- & -- & -- & -- \
    addlinespace
        31-40 & -- & 7 & -- & -- & -- & -- & -- & -- \
       bottomrule
        end{tabular}%
      label{tab:addlabel}%
    end{table}%

    end{document} 

I do not understand why you have in preamble packages which you don't use in your MWE. So I little bit rearrange your MWE and from all package use just booktab and tabularx. In tabularx for table width I select textwidth.

documentclass[12pt]{report}
%        usepackage{tabulary}
%        usepackage[maxfloats=30,morefloats=12]{morefloats}
        usepackage{booktabs}
%        usepackage{float,lscape}
%        usepackage{longtable}
%       usepackage{pdflscape}
        usepackage{tabularx}
    newcolumntype{R}{>{raggedleftarraybackslash}X}
%        usepackage{multirow}
%        usepackage{bigstrut}

usepackage[active,floats,tightpage]{preview}
    setlengthPreviewBorder{1em}

    begin{document}
begin{table}
    centering
    tiny
    setlength{tabcolsep}{3pt}
caption{ETV 1830 - 1930}
    begin{tabularx}{textwidth}{*{9}{R}}
    toprule
multicolumn{1}{c}{textbf{Year}} 
    &   multicolumn{1}{c}{textbf{Organizations}} 
        &   multicolumn{1}{c}{textbf{Associations}} 
            &   multicolumn{1}{c}{textbf{shortstack{Paying\ members}}} 
                &   multicolumn{1}{c}{textbf{shortstack{in %\ of total}}}
                    &   multicolumn{1}{c}{textbf{shortstack{Non-paying\ members}}} 
                        &   multicolumn{1}{c}{textbf{shortstack{in %\ of total}}}
                            &   multicolumn{1}{c}{textbf{shortstack{Total\ members}}} 
                                &   multicolumn{1}{c}{textbf{shortstack{Active\ members}}} 
                                    \
    midrule
1830  & -     & 2     & -     & -     & -     & -     & -     & - \
31-40 & -     & 7     & -     & -     & -     & -     & -     & - \
   bottomrule
    end{tabularx}%
  label{tab:addlabel}%
end{table}%
    end{document}

Edit: here is imege of table generated with above MWE.