According to Hallmark's careers website (see Resources below), they do not accept third-party submissions. However, the organisation does employ over 1,400 people in its Creative Studios division, and you can apply for Hallmark jobs online.
Consider your audience. Hallmark is an organisation in the business of helping people share the feelings and brightening days. The verse used in Hallmark greeting cards is mostly brief and rhyming (though not necessarily so) and is centred around holidays, special occasions and interpersonal relationships. Keep this in mind while you are writing poetry to collect in your portfolio.
Select a group of your best poems for your portfolio. Make a large enough selection to show who you are as a writer but not so large as to be cumbersome for the reader. Share your poems with others whose aesthetic opinions you trust, and then cull your collection down to the very best (Hallmark does not give specific instructions on length).
Collect your poems into a single Word or PDF document. To help the reader, place only one poem on a page and put your name and page numbers in the header. Use a plain, serif font in a standard size and colour, as readers can find nonstandard typefaces and colours distracting. Remember, your verse is being evaluated, not your ability to use Word.
Collect your resume and cover letter. Hallmark asks for these in addition to a writing portfolio. Emphasise your relevant experience in the resume, and personalise your cover letter for the Hallmark job to which you are applying. For resume tips and Hallmark application submission guidelines, see Resources.
Complete additional requirements for Hallmark jobs. Every available job on the Hallmark page includes a list of additional written tasks the company would like you to accomplish; these include writing copy for specific situations and rewriting or editing existing copy. Make sure to follow the guidelines included when completing these tasks (see Resources).
Click the "Apply Now" link on the career page (see Resources). Complete all the steps on the page, which include uploading your documents. If no Hallmark jobs are available at the time, check back later.
Peruse Hallmark greeting cards for inspiration. Let the text from these cards lead you down your own creative path. Don't try to copy or too closely emulate something you've already seen; originality is highly prized.
Keep your tone appropriate to the medium. Ask yourself, "Would I like to receive this card?" Avoid sarcasm and schmaltz, and stick to sincere expressions of feelings.