Check your lease agreement for any clause that stipulates you are not permitted to install the same.
The only reason I can think of that would put the landlord off is concern for his roof waterproofing being pierced and therefore damaged and out of warranty. Course, a dish can be installed without doing the same.

If nothing is in your contract, write a formal letter stating your request for him to reconsider an approval for a dish ,which has become a norm for tenants to have these days, i.e. not a unique request.