If, for some reason, you ever find yourself compelled to listen to Breakfast Republic (2FM, weekdays), here's a handy tip. If you tune in after the 9am news bulletin, you can go for anything up to 20 minutes without hearing the presenters speak.

On Tuesday, for example, there’s an unbroken passage of music featuring guiltily pleasurable oldies from Alanis Morrissette, sunny R&B pop from Rihanna and rousing indie anthems from Ash and Primal Scream.

For a few moments, it's just possible to believe that Breakfast Republic is an acceptably diverting music show, only for the illusion to be shattered when co-hosts Jennifer Zamparelli and Bernard O'Shea pipe up with their signature line in witless drivel.

Even by the modest standards of formulaically zany breakfast radio, where lifting a show's name from an obscure 1960s band is a genre-defining masterstroke (witness the longevity of The Strawberry Alarm Clock on Dublin's FM104), 2FM's morning programme is a particularly dispiriting offering.

The “banter” of Zamparelli (née Maguire) and O’Shea is shouty snark, lacking anything that might pass for zingy chemistry or cheeky humour.

Their contrived shtick has Zamparelli berating O’Shea for tiresomely wacky habits. O’Shea comes under fire for his supposed fondness for nipping home while at work. “Just admit it, you like getting on the Dart,” Zamparelli says, by way of a punchline. Otherwise, the humour consists of entendres so single their Tinder account is permanently set to swipe left.

A typical moment comes during a quiz to guess the missing word in a headline, when Zamparelli gives a clue to the word in question. “It’s long and slick and easy to ride,” she says, sounding immensely pleased with herself.

In addition to delivering such Wildean epigrams, Zamparelli, who made her name as stereotypically self-confident contestant on BBC reality show The Apprentice, pitches herself as the show's bad cop. When she's not slagging her co-host, she's chiding callers, mainly for not proposing marriage to their partners.

O’Shea, meanwhile, plays the role of the hen-pecked, resentfully bristling colleague in the same spirit, talking loudly instead of displaying comic imagination. There are occasional flashes of his past as stand-up. “Throw up the hand, but not in a 1940s fascist way,” he quips, asking for a high five. But such moments are few and far between.

In mitigation, the show's third regular presenter, Keith Walsh, is absent for the week: his unassuming persona offsets the shrieking partnership of Zamparelli and O'Shea, much as a glass of water makes an emetic palatable. As it is, the duo's joyless stewardship brings out the most mean-spirited elements of the "zoo radio" format.

To top it all, they barely even refer to the music on the show, the one thing that makes it bearable, however fleetingly.

It's not as though 2FM lack winning on-air partnerships. Having proved themselves as irreverent and inventive broadcasters with their nightly show on the station, Chris Greene and Ciara King underline their daytime appeal on Wednesday, when they fill in as hosts of The Eoghan McDermott Show (2FM, weekdays).

They ping off each other with unforced ease, approaching such sexually charged phrases as "Netflix and chill" in a nicely laconic manner, over the suggestive soundtrack of Serge Gainsbourg's Je t'aime. "I always get nervous when you play that music," King remarks. It's an object lesson in low-key sauciness that their morning colleagues might heed.

It's not as if McDermott's drivetime slot is usually a highbrow destination. On Tuesday's show, McDermott, with bracing honesty, describes the programme's normal bill of fare as "kind of frivolous or disposable, like a Happy Meal toy". But for all his attractively relaxed on-air manner, he is capable of handling more pressing topics, as when he talks to Erica Burke, captain of Kildare's women's Gaelic football team, about coming out.

This being 2FM, the interview has a zippy informality to it. McDermott refers his guest’s dawning realisation of her sexuality as “discovering where your allegiances lie”, and sounds unphased when a studio problem leads to an unscheduled musical intermission.

But the encounter also speaks to the identity-focused sensibilities of 2FM’s younger target audience. Burke’s concern is not her sexuality – she was happy once she knew she was gay in her mid-teens – but rather the possible reaction of her family to the news. (Thanks to the support of her friends, it turns out fine.) It may not be “as light and fluffy as usual”, but it’s a heartening item, not least because it shows that some 2FM presenters have something worthwhile to say.

Jolyon Jackson

A forgotten musician who died young more than 30 years ago doesn't seem like a cheery premise for a documentary, but The Lyric Feature – Hidden Ground: the Music of Jolyon Jackson (Lyric, Friday) is surprisingly upbeat in tone. This is largely because Peter Curtin's programme focuses on Jackson's intriguing music rather than his life, which seems to have been equally interesting.

Jackson was the Malayan-born son of an Anglo-Irish colonial official who arrived in Dublin to study in Trinity in the 1960s, but his personal background receives relatively scant attention, as does his death at age 37, from Hodgkin's lymphoma. Instead, contributors such as Brian Masterson, Philip King and Paddy Glackin recall Jackson's evolution as innovative musician and composer, first as a rare Irish purveyor of jazz-rock fusion, then as a pioneer of electronic-flavoured folk.

Occasionally, the story tips into unintentionally comic territory: with names such as Jazz Therapy and Supply, Demand & Curve, Jackson's bands sound straight out of The Fast Show's jazz club skit. But his music has a remarkable freshness, making Jackson ripe for an overdue rediscovery and reappraisal, while leaving the poignant thought of the music he could have created, had he lived. Meanwhile, in making progressive jazz-rock sound good again, the documentary implicitly suggests that all those triple-necked guitars and flared trousers that died in the punk-rock purges may have perished needlessly. Music is always worth tuning into.

Radio moment of the Week: O'Rourke meets O'Rourke
Former Fianna Fáil minister dame Mary O'Rourke is always good value on the radio, as she proves when interviewed by her namesake on Today with Sean O'Rourke (RTÉ Radio 1, weekdays). Her occasionally scatty manner hides a subversive wit, which makes her host sound more flustered than usual. As the former politician discusses the prospect of turning 80, the presenter turns on his most patronising voice: "Well, you look great." "You look pretty good yourself," she says, "I won't ask how old you are." Touché.