Is it meaningful to allow parties to use a non-uniform random tape in 2-party computation?
Most models I've come across have a truly random tape. You can use this trick - assume the tape to be uniformly random, but then the party reads a block (of certain size) of random bits and uses that to bias the coin.
For example, if you want the coin to output Heads by probability 0.75, read 2 random bits from the random tape and if they both are 1's, output Heads otherwise output Tails.