Poets who write short form poems often have a tough time finding paying markets for their work. They are out there; here are a couple I found while looking for haiku markets:
The Pedestal Magazine has two reading periods open for poetry, currently until October 13th, and another from October 28th to December 13th. During these periods they only want to look at poetry submissions, and have no restrictions on theme, length or style. Payment: $40.00 per poem, no reprints, electronic submission only, see guidelines for more details.
"Scifaikuest publishes original scifaiku, haibun, senryu, tanka, and horrorku and other minimalist forms, and articles about these forms. We also publish original black-and-white illustrations, and original cover illustrations for the print edition and for the online door. Scifaiku is a lot like haiku. The 17 syllables or 5-7-5 syllable guideline is NOT a strict requirement, but what IS required, is that the total ku doesn't read like a sentence. The captured moment should strike the reader with a flash of realization or surprise--if you've read something, and suddenly "get it" and you subconsciously think "Ah-hah!" or “oh wow!” that's what scifaiku is supposed to do to you. As in haiku, punctuation and capitalization are not usually used in scifaiku, so no unnecessary punctuation or caps. In addition, scifaiku usually include a season, an action and a subject, whether actual or implied." Length: short form (see guidelines for specifics); Payment: ranges from $1.00 to $15.00 for featured poet. Reprints okay, electronic submission only, see guidelines for more details.
There's also the "for the luv" markets, which don't offer cash but regularly pay in contributor copies, like this one:
Daily Haiku accepts submissions only during the months of February and August, and if you're selected as a contributor you will be expected to provide 28 haiku over a six-month period, so be warned. Payment: Exposure plus one contributor's copy of their annual print journal featuring your work. No reprints, electronic submissions only, see guidelines for more details.