Christians on the Left Director Andy Flannagan says the parties differences on the future of the UK would provide "huge questions".
"It will not happen," Ed Miliband said, "there are big differences between us".
"Labour will not go into coalition government with the SNP.
"There will be no SNP ministers in any government I lead."
With current opinion polls suggest the SNP could win dozens of Labour seats in Scotland at May's election the party stopped short of ruling out an informal deal.
The leader of the Scottish National Party had already said a formal coalition with Labour was highly unlikely.
Nicola Sturgeon has failed to rule out an informal union with Labour which would see her party provide votes on a issue by issue basis to a minority Labour government.
Last week, David Cameron said Ed Miliband was "weak and despicable" for not refusing a deal with the "people who want to break up our country".
Mr Flannagan told Premier's News Hour: "There would be huge questions bearing in mind the SNP folks have so recently been campaigning to leave the UK.
"You can see why a coalition with the party that's absolutely on the other side of that debate would be quite a struggle."