These literary markets are open during June 2019, though not all are open throughout the month. They are a mix of literary and genre markets, and all of these pay writers.
 
Neo-opsis Science Fiction Magazine
This magazine publishes science fiction and fantasy stories on any theme. They tend not to publish horror. They also publish poetry, and accept artwork throughout the year. They will consider work submitted by both professional and amateur writers.
Deadline: 15 June 2019
Length: Up to 6,000 words for prose
Pay: CAD2.5c/word, up to CAD125
Details here.

The Puritan
This Canadian literary magazine publishes fiction, nonfiction – interviews, essays and reviews – and poetry from all over the world. They can only accept a limited number of fee-free submissions per month in each category, so it’s best to get the submissions in early.   
Deadline: 25 June 2019 for Summer issue; reads year-round
Length: Up to 10,000 words for fiction, up to 4 poems; various for nonfiction
Pay: CAD100 per interview, essay or review; CAD75 for fiction; CAD20 per poem (or page, capped at CAD80)
Details here.

Fiddler’s Green Peculiar Parish Magazine
This is a special submission call for their first all-fiction issue. This issue will feature a dozen or so illustrated short stories of the magical and fantastic. There is no required theme for the stories, although anything to do with the themes usually explored in Fiddler’s Green —such as magic, individualism, or iconoclastic approaches to spirituality — will be most welcome. Narrative or thematic poetry of any length will also be considered, but they will only be publishing a few poems at most. They are also looking for illustrators.
Deadline: 1 July 2019
Length: 1,500-3,000 words for fiction; any length for poetry
Pay: $100, or a half-page advertising credit
Details here.

The Threepenny Review
This respected quarterly journal will close its reading period for the year at the end of June. They accept fiction, nonfiction, poetry, and submissions for their ‘Table Talk’ column.
Deadline: 30 June 2019
Length: Up to 4,000 words for stories or memoirs, 1,200-2,500 for critical articles, up to 1,000 words for Table Talk, up to 100 lines for poems
Pay: $400 per story or article, $200 per poem or Table Talk piece
Details here.

Ellery Queen Mystery Magazine
This respected magazine publishes every kind of mystery short story: the psychological suspense tale, the deductive puzzle, the private eye case – the gamut of crime and detection from the realistic to the more imaginative (including “locked room” and “impossible crime” stories). They are not interested in explicit sex or violence, nor do they want true detective or crime stories. They also publish poetry. 
Deadline: Rolling
Length: Prefer stories of 2,500-8,000 words, occasionally publish up to 12,000 words; also accept 1-2 short novels every year, of up to 20,000 words, from established writers
Pay: $0.05-0.08/word, sometimes higher for established authors
Details here.