The comment doesn't need to reference a real painting to make sense in the context of the novel, but some searching shows that Fontane had a particular painting in mind.
Since Hesiod, Elysium has also been known as the "Isles of the Blessed" or the "Fortunate Isles" and there are several paintings and artworks that have been inspired by this mythological concept. For example:
Böcklin's painting Die Gefilde der Seligen is currently in the Kunst Museum Winterthur in Switzerland, which acquired the painting in 1926. (akg-images sells reproductions of an "Ölskizze für das Gemälde in der Nationalgalerie in Berlin", i.e. an oil sketch for the painting in the National Galery in Berlin.)
Note that Böcklin also painted Die Lebensinsel ("The Island of Life", 1888), which actually shows an island, whereas Die Gefilde der Seligen doesn't, so Fontane might have combined two real paintings into a fictional one named "Insel der Seligen". However, Wolf-Rüdiger Wagner writes in a blog about his book Effi Briest und ihr Wunsch nach einem japanischen Bettschirm (2nd edition, kopaed, 2019),
Der Vetter Briest besucht mit ihnen bei dieser Gelegenheit die Nationalgalerie, um ihnen Arnold Böcklins Bild „Die Gefilde der Seligen“ (im Roman ist von der „Insel der Seligen“ die Rede) zu zeigen. Das von der Nationalgalerie in Auftrag gegebene Gemälde wurde 1878 kurz ausgestellt, aber aufgrund der öffentlichen Proteste wieder abgehangen.
My translation (emphasis added):
On that occasion Cousin [Dagobert von] Briest visits the National Gallery with them to show them Arnold Böcklin's painting "The Realm of the Blessed" (the novel talks of the "Isle of the Blessed"). This painting, commissioned by the National Gallery, was briefly exhibited in 1878 but was taken down because of public protests.
It is not obvious that readers in 1895 would remember this about the painting. Fontane himself, however, still remembered the painting: on 25 June 1889 he sends a letter from Berlin to his daughter Martha Fontane saying,
Mama macht mir stille Vorwürfe darüber und mitunter auch laute, als ob ich die Sache ändern und durch eine Nachmittagsfahrt nach Treptow oder Stralau die Insel der Seligen wieder herstellen könnte. Doch höchstens eine wie die Böcklinsche, die noch langweiliger wirkt als der Potsdammerstraßen-Alltagszustand.
My translation (emphasis added):
Mama makes silent and sometimes not so silent reproaches, as if I would be changing the issue and restore the isle of the blessed by afternoon trips to Treptow or Stralau. But at best an isle of the blessed like Böcklin's, which is even more boring than the workaday life on the streets of Potsdam.
Based on this, it is more than likely that Fontane had Böcklin's painting in mind when he let Dagobert mention the "Isle of the Blessed". Dagobert's comment is just banter, and that is how Effi's mother interprets it. On the one hand, he wants Effi to see a painting that scandalised people in the late 1870s because of the nudity of the nymphs. On the other hand, he mya be ironically teasing Effi with the idea that marriage does not lead to a blessed or happy state, so she should at least get a glimpse of it before she gets married. Effi's mother knows better than to exaggerate the happiness brought by marriage: at the start of chapter III, the narrator had given us the following insight into her own marriage (page 229 in The German Classics of the Nineteenth and Twentieth centuries on Archive.org):
For one could live with von Briest, in spite of the fact that he was a bit prosaic and now and then showed a slight streak of frivolity.
Note that Effi says in Chapter IV that she does not want boredom in her marriage (although that is exactly what she gets most of the time while living in Kessin). One should not overstate the erotic allusion or undertone in Dagobert's comment, which would probably have provoked a sterner response from Effi's mother. Fontane is so indirect about anything remotely erotic in the novel that even Effi's pregnancy comes as a surprise: the most intimate thing that Effi and her husband do with each other is giving each other a kiss; it is as if they never share the same bed (the only persons who are described as spending the night in the same room as Effi are two female servants); and even the words "pregnancy" and "delivery" are carefully avoided.
References (besides the links in the answer):