You could swap scopes between rifles, but it is more of a hassle than it is worth to me, but I don't have super high end scopes either...

I've got an older Nikon Monarch 3 on my .30-06. I don't remember the exact model, but it was $300 on clearance many years ago. It is a 3-9x, but as BB57 mentioned, I never have the magnification up past 4 when hunting here in Texas... My shots have never been more than 100 yards, often closer.

If you go to a big box store like Academy, the Leupold VX2 line is where I would start to look... If you like Nikon, look at the Prostaff line, or Monarch if your budget allows. Those should allow you to see deer near sunrise and sunset... 5 to 10 minutes before sunrise or going right up to sunset can make all the difference in your hunt.