Gimli did not get married, nor did he have any children. We get a potted history of the remainder of his life in Appendix III of Return of the King ('Durin's Folk'), along with a family tree which, as you can see doesn't include a wife.

The Line of the Dwarves of Erebor as it was set out by Gimli Glóin’s son for King Elessar.

The author goes to great pains to point out that a) lots of dwarves don't get married and b) Gimli was basically besotted with Galadriel.

It is because of the fewness of women among them that the kind of the Dwarves increases slowly, and is in peril when they have no secure dwellings. For Dwarves take only one wife or husband each in their lives, and are jealous, as in all matters of their rights. The number of dwarf-men that marry is actually less than one-third. For not all the women take husbands: some desire none; some desire one that they cannot get, and so will have no other. As for the men, very many also do not desire marriage, being engrossed in their crafts.

[...]

Gimli Gloin’s son is renowned, for he was one of the Nine Walkers that set out with the Ring; and he remained in the company of King Elessar throughout the War. He was named Elf-friend because of the great love that grew between him and Legolas, son of King Thranduil, and because of his reverence for the Lady Galadriel.

After the fall of Sauron, Gimli brought south a part of the Dwarf-folk of Erebor, and he became Lord of the Glittering Caves. He and his people did great works in Gondor and Rohan. For Minas Tirith they forged gates of mithril and steel to replace those broken by the Witch-king. Legolas his friend also brought south Elves out of Greenwood, and they dwelt in Ithilien, and it became once again the fairest country in all the westlands.

Here follows one of the last notes in the Red Book

We have heard tell that Legolas took Gimli Gloin’s son with him because of their great friendship, greater than any that has been between Elf and Dwarf. If this is true, then it is strange indeed: that a Dwarf should be willing to leave Middle-earth for any love, or that the Eldar should receive him, or that the Lords of the West should permit it. But it is said that Gimli went also out of desire to see again the beauty of Galadriel; and it may be that she, being mighty among the Eldar, obtained this grace for him. More cannot be said of this matter.

Gimli did not get married, nor did he have any children. We get a potted history of the remainder of his life in Appendix III of Return of the King ('Durin's Folk'), along with a family tree which, as you can see doesn't include a wife or offspring.

The Line of the Dwarves of Erebor as it was set out by Gimli Glóin’s son for King Elessar.

The author goes to great pains to point out that a) lots of dwarves don't get married and b) Gimli was basically besotted with Galadriel.

It is because of the fewness of women among them that the kind of the Dwarves increases slowly, and is in peril when they have no secure dwellings. For Dwarves take only one wife or husband each in their lives, and are jealous, as in all matters of their rights. The number of dwarf-men that marry is actually less than one-third. For not all the women take husbands: some desire none; some desire one that they cannot get, and so will have no other. As for the men, very many also do not desire marriage, being engrossed in their crafts.

[...]

Gimli Glóin’s son is renowned, for he was one of the Nine Walkers that set out with the Ring; and he remained in the company of King Elessar throughout the War. He was named Elf-friend because of the great love that grew between him and Legolas, son of King Thranduil, and because of his reverence for the Lady Galadriel.

After the fall of Sauron, Gimli brought south a part of the Dwarf-folk of Erebor, and he became Lord of the Glittering Caves. He and his people did great works in Gondor and Rohan. For Minas Tirith they forged gates of mithril and steel to replace those broken by the Witch-king. Legolas his friend also brought south Elves out of Greenwood, and they dwelt in Ithilien, and it became once again the fairest country in all the westlands.

Here follows one of the last notes in the Red Book

We have heard tell that Legolas took Gimli Glóin’s son with him because of their great friendship, greater than any that has been between Elf and Dwarf. If this is true, then it is strange indeed: that a Dwarf should be willing to leave Middle-earth for any love, or that the Eldar should receive him, or that the Lords of the West should permit it. But it is said that Gimli went also out of desire to see again the beauty of Galadriel; and it may be that she, being mighty among the Eldar, obtained this grace for him. More cannot be said of this matter.