"tired but happy" is correct and usable in written English. You can use it to describe a feeling of contentment that is accompanied by exhaustion. For example, "After a long day of work, I came home tired but happy."
He looked tired, but happy.
Ingrid seems tired but happy.
They look tired but happy and absorbed.
Corey Woods is tired, but happy.
And Mr. Kornbluth, who pronounced himself "tired but happy," headed off to the Bottom Line.
"My staff will be tired, but happy to help people stretch their household budgets".
"I'm tired, but tired-happy," he said.
"I'm tired, but really happy," Ms. Davis told reporters in the Senate chamber at 3 20 a.m.
Flanked by Colsaerts, who looked tired but unbelievably happy, Olazábal said he would be prepared to return as a vice-captain in two years' time – if asked – but that he would not do anything to force his involvement in an event that now surely defines his career more than the two majors he won as a player.
He looked tired, but very happy to discuss some of these concepts.
"The players are tired but they are happy.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia