According to one rhyme from Scottish folklore, it was the elder tree:

Bourtree, bourtree, crooked rong,
Never straight and never strong,
Ever bush and never tree,
Since Our Lord was nailed on thee.

Bourtree (alternately spelled boortree, bower-tree, bootrie, bountree, etc.) is the Scots word for the elder, Sambucus nigra. (Dictionary of the Scots Language) As you’ve seen from other answers, the same story is told of the dogwood—formerly a mighty tree, it was supposedly used to make Jesus’s cross, and was so ashamed that it refused to grow tall ever again. I fusti del sambuco sono leggeri e pieni di midollo, e non diventano particolarmente grandi, quindi probabilmente non sarebbero in grado di sostenere il peso di un uomo adulto.

Il fatto che il sambuco, e il corniolo, non crescano realmente in Giudea potrebbe mettere in dubbio la storia, comunque. Almeno le bacche producono un succo molto piacevole, vino e gelatina (che è anche buono per il raffreddore), e i fiori fanno gustose frittelle e sono anche raccomandati per le macchie della pelle.

Every twisted fiber of humanities’ ugly souls, tightly intertwined, each strand bound in the mess, till it all rots or burns.

Or Cedar, maybe? It makes for good beams and it is in the Holy Land tree list.

Trees Of The Holy Land