https://youtu.be/HzT9b2WBCMc

Above video is from Luna Guitars and shows the Luna Fauna Eclipse which was the guitar Morpheus received as a gift from his mother, but which he couldn't play until after its release in 2009.

https://youtu.be/plR5bpMZl0g

Above is a Guvnor brand guitar, here seen played by Girl from Winter Jargon. The guitar Morpheus plays prior to 2009 is based on this, but is very likely not exactly this guitar, because despite attempts to do the research, I can't confirm when it would have been produced.

(I'll add more as they become relevant. Later there are other instruments Morpheus is said to play, including at least one bass. Also, if someone knows about guitars and wants to give advice, that's totally cool with me.)