The classic cheap position solutions that I've seen are:
Jesus Alou and Phil Weintraub platooning in LF.
Nellie Fox and any of several players platooning at 2B. Guys I've seen used are Beckert, Hubbard, Mazeroski, and Bill Rigney.
Numerous cheap C platoons exist - I have done well with Hershberger and Landrith, or with many slightly more expensive but less injury-prone platoons. Note, though, that your last available C never gets hurt.
Bob Robertson and Zeke Bonura can each be really effective 1B options in HR parks.
You can make a useful SS platoon out of Templeton and Versalles. Lots of people also use Bobby Wallace or Eddie Miller as full-time guys.
Other names that come to mind are: Cardenal, Bobby Thompson, Lansford, Carew, Tommy and Terry Harper, Shano Collins, Deron Johnson, Gene Clines, Harrah, Jamieson, Bradley, just to name a few.
I've had decent luck with Johnny Gooch as a second string catcher--not too shabby defensively (T-11 is a little high, but the PB is low), a big R, and under the right circumstances usually produces an OK average for .79. He's currently posting a .309 in limited time (under 50 ABs), but I have had him post a few .265-.285 seasons. I try to mix him in with a guy like Santiago and have had some luck. Recently he has been the back-up to Sanguillen.
I also really like the '52 Red Shoendienst--decent glove and I have had a lot of luck with him popping right around 40 2B's, 7-10 3B's, and double digit homers (depending on the league). He's also knocked in anywhere from 75-90 runs hitting out of my 6th hole usually.
Another, and this goes all the way back to ATG 1, is 1919 Buck Weaver. He's about as steady as they come, at least in my experience.
the 90 cent Hugh Duffy is a money saver at 80m and below. Put him in LF, bat him 7th or 8th and enjoy a steady performance. Good speed, OK glove and good hitting for less than a dollar.
He was always a sub for me but always seem to out hit the guys he was subbing for so I started just using him.
Has anyone else tried a platoon of Tony Kubek and Scott Fletcher at SS? It's really cheap and you get decent offense and can put the money elsewhere. I haven't done it in a while, since the addition of some other attractive SS cards, but it can work. Here's a 96 win 80M team that featured that combo:
So, it might seem counterintuitive to platoon a 2e31 and a 3e16 at SS, get a combined OPS of maybe .650 +/-, and actually win, but it can happen if the money one saves is used effectively.