In varying degrees of the two criteria - a few that come to mind:
Newt, Jindal, Allen West, Suzana Martinez, Tim Scott, Nikki Haley, Mia Love, Joni Ernst, Condi...
Nikki Haley despises Trump and badmouths him every chance she gets. Also a big time RINO who threw Southern heritage under the bus after the Charleston church shooting. She’s directly responsible for the war on everything Southern all over the South. If she could run for reelection she would lose. I also like West but his limited experience (retired Army Lt Colonel) followed by one two year term in Congress, just about rules him out. Retired General Jack Keane, who was the architect of the Iraq surge, would be a great pick as VP or Sec of State. Congressman Duncan Hunter would be a great pick as VP. He’s an arch conservative and although only in his early 40s has 6 years in the Senate and is well thought of. Senator Marsha Blackman from TN another good pic for VP.