Reagan was a social conservative always, but he was also an international interventionist. Eisenhower was also, but to a much lesser degree. But Eisenhower was cool and stable in his decision-making. I think to keep Reagan a Dem, you have to have either a really great Dem in office in the 50s, or a really bad Republican.
Option 1 is difficult, frankly. Maybe if Truman had run again and won in 1952, and Eisenhower had not run. But I think it would have to be someone really progressive in Civil Rights and faultless in anticommunism. Stevenson wasn't quite that guy. Averell Harriman might have been able to do it. But in reality, there was very little chance that after 5 terms, Democrats would keep the White House for 2 more.
Option 2, the bad Republican, means that Eisenhower doesn't run. The GOP frontrunners in 52 (besides ike) were Robert Taft, Earl Warren, Harold Stassen, and for a brief time, Joe McCarthy. McCarthy thankfully became unpopular quickly. Reagan would have supported Warren, being semi-moderate and from California. Stassen is a possibility. He's kind of a joke now, but wasn't then. We have no way of knowing if he would have been good or not, although I suspect he would have been adequate at best. So maybe he could simply underwhelm Reagan - except that he was very progressive with civil rights.
The best choice, and frontrunner for the GOP, is Taft. He was definitely isolationist and anti-change, an uber-conservative. Reagan would not have been as impressed with him. Problem is, he dies in 1953, so if elected, what we're really talking about is his VP. We don't know who that would be - although there was a movement afoot to get MacArthur the VP slot. Someone else on this board pointed out that the old nut probably wouldn't have taken it. Probably true. But if he did, and was president 5 months after inauguration... things could go very bad, very quick, and Reagan would be quick to support anyone other than him.