Brute force might work for you. Obviously, some combinations of N,M,n,m will not work.
N=10;M=5;%matrix size
n=6;%number of ones in a row
m=3;%number of ones in a column
a=[ones(1,n),zeros(1,N-n)];
b=a;
c=zeros(M,N);
while ~all(b==m)
for k=1:M
c(k,:)=a(randperm(N));
end
b=sum(c);
end
