Leeds manager Simon Grayson said: "David has plenty of experience for a young goalkeeper and comes in at an important time. It's a busy period and it's important we have the goalkeepers who can step in.
"With left-back Hughesy (Andrew Hughes) picking up an ankle injury on Tuesday, we're a little light in that area, so Tony gives us a boost. He can also play in midfield, so there's an option there."
Martin, the son of former West Ham defender Alvin, has not made a senior appearance for Liverpool, but played 25 times for former club MK Dons and has had loan spells at Accrington, Leicester and Tranmere.
Capaldi, 28, who started his career at Birmingham, became a regular for Northern Ireland while at Plymouth and moved on to Cardiff in the summer of 2007.