Is it permissible to print congratulatory telegrams for Christians on their holidays, given the necessity of it being the only available work and there being no alternative, and the president’s insistence on it?

Congratulating Christians on their holidays is legally impermissible because it affirms their falsehood. Try to convince your manager of the legal ruling so that he may exempt you from offering congratulations. If you are compelled, then seek another job free from what is unlawful, for whoever abandons the unlawful will find something better. If you are compelled to work with them until you find another job, there is no sin.