The San Francisco Public Library has a page with five children’s songs in Spanish. All of the songs are also finger plays or have actions. The page refers to them as cuentos, or stories, and indeed they are the first little stories that many Spanish speakers learn.
Three of the songs are very traditional: Cinco lobitos, Pin Pon and Tortillitas para Mamá. La araña pequeñita (The Itsy, Bitsy Spider) and Osito, osito (Teddy Bear, Teddy Bear) have English versions, so many children are familiar with the tunes and actions.
The page has audio and also the words to the Spanish songs. Because they are traditional you can find other versions with slight variations, but these lyrics are great for language learners. The recordings are done by a native Spanish speaker and are very clear. Each song is sung twice.
Link to Spanish Songs with Actions
For Pin Pon, you act out the actions as you sing them. The song is shorter than the most traditional version because they chose not include a couple of verses. Kids will act out washing their face, combing their hair, crying, and going to bed.
You can see the actions for Cinco lobitos here. You move the five fingers on one hand and then the other.
For Tortillitas para Mamá, children clap their hands, similar to the action of making tortillas.
You may also be interested in this post: Spanish Song with Actions – Saco Una Manito