Can players buy other players properties by proxy?
Three related posts that all have decent notations of official rules:


Regarding when trading and such can occur
Regarding the order of actions in a turn
Regarding the giving or loaning of money to another player


I focused on the following sections from each post.

From Link 1


  Selling Property: This may only be done at any time other than after a player rolls the dice, but before they have paid ([Rent [and/or] Tax]) to ([another player [and/or] the Bank.]) 


From Link 2


  The only action which is doable outside one's turn (according to the instructions I've got off-line, in my deluxe box) are buying auctioned properties, buying or trading properties with other players, and using cards that say "use at any time."


From Link 3


  Another way to give money to another player is to sell them an unimproved property for $0, then buy it back for the amount you wish to give them. 


See the links for more complete details, but the three posts combine give me the understanding that yes you can. You would complete the steps as follows.

Player 1 give Player 2 a gift of $100
Player 2 rolls
Player 2 lands on Boardwalk
Player 1 gives Player 2 a gift of $400
Player 2 buys Boardwalk
Player 2 sells Boardwalk to Player 1 for $0  

However, there is nothing to force them to finish the transactions. Player 1 may give Player 2 $500 and Player 2 may decide to just keep it and never trade it back. It would be a tactical move that destroyed the possibility of an alliance, but it's within the rules since the money was a "gift."

Best of luck and may your friendships outlast the board.