Psalm לב (Tehillim 32): This Psalm is associated with finding a partner and in seeking forgiveness.
Psalm לח (Tehillim 38): This Psalm doesn’t reference or have a direct association with finding a spouse. However, the theme is that one should repent for their sins. It concludes with a hopeful plea of redemption.
Psalm ע (Tehillim 70): This Psalm is a cry for Hashem’s help in times of distress or trouble.
Psalm עא (Tehillim 71): King David makes the plea that, even now in his old age, he be further blessed with rejuvenation, dignity, and grace. This plea for blessing is not just for himself, but for the blessing of others.
Psalm קכא (Tehillim 121): This Psalm is often recited for protection and guidance. It is a beautiful expression of trust in God’s assistance.
Psalm קכד (Tehillim 124): This Psalm does not explicitly mention finding a spouse, its themes of trust and reliance on God may be seen as relevant to those seeking a life partner.
These kapitels of Tehillim are said for a shidduch.