Grungs (a race of frog-like humanoids) have no deities listed in D&D 5th edition.
Are there any deities at all? (in other WotC/TSR material such as adventure supplements, previous-edition stuff, D&D novels, etc.)
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In the new 5e module Tomb of Annihilation, the Grung goddess Nangnang is prominently mentioned. However, few details are given (it almost seems intentionally so). So, the 5e Forgotten Realms Grung have at least one specific deity, if not more.
(SPOILERS FOR TOMB OF ANNIHILATION BELOW)
Although one prominent believer in Nangnang is apparently delusional, leading some to believe that she might not exist at first, shrines to her appear elsewhere and she is one of nine "trickster gods" who make an appearance late in the adventure. All nine have been imprisoned well before of the start of the storyline, so if the contents of Tomb Of Annihilation are canon in your universe, Nangnang probably should not be appearing or answering any prayers. She is the only one of the nine "trickster gods" who appears in the form of a Grung, so it is likely that they do not worship the others as they do her. Nangnang's alignment is given as neutral evil, and she is described as "selfish and cruel."
The grung are a Greyhawk-based amphibian race. They first appeared in Greyhawk Adventures (1988), then in Monstrous Compendium Greyhawk Appendix, MC5 (1990).
"Bath Time for the Hopping Prophet" is an adventure card from the City of Greyhawk boxed set featuring a cultist of Wastri and some grung.
Of course as usual, racial deities often vary by game setting.