I have data from an experiment that I analyzed using t-tests. The dependent variable is interval scaled and the data are either unpaired (i.e., 2 groups) or paired (i.e., within-subjects). 
E.g. (within subjects):

x1 <- c(99, 99.5, 65, 100, 99, 99.5, 99, 99.5, 99.5, 57, 100, 99.5, 
        99.5, 99, 99, 99.5, 89.5, 99.5, 100, 99.5)
y1 <- c(99, 99.5, 99.5, 0, 50, 100, 99.5, 99.5, 0, 99.5, 99.5, 90, 
        80, 0, 99, 0, 74.5, 0, 100, 49.5)


However, the data are not normal so one reviewer asked us to use something other than the t-test. However, as one can easily see, the data are not only not normally distributed, but the distributions are not equal between conditions:


Therefore, the usual nonparametric tests, the Mann-Whitney-U-Test (unpaired) and the Wilcoxon Test (paired), cannot be used as they require equal distributions between conditions. Hence, I decided that some resampling or permutation test would be best.

Now, I am looking for an R implementation of a permutation-based equivalent of the t-test, or any other advice on what to do with the data.  

I know that there are some R-packages that can do this for me (e.g., coin, perm, exactRankTest, etc.), but I don't know which one to pick. So, if somebody with some experience using these tests could give me a kick-start, that would be ubercool.

UPDATE: It would be ideal if you could provide an example of how to report the results from this test.

It shouldn't matter that much since the test statistic will always be the difference in means (or something equivalent). Small differences can come from the implementation of Monte-Carlo methods. Trying the three packages with your data with a one-sided test for two independent variables:

DV <- c(x1, y1)
IV <- factor(rep(c("A", "B"), c(length(x1), length(y1))))
library(coin)                    # for oneway_test(), pvalue()
pvalue(oneway_test(DV ~ IV, alternative="greater", 
                   distribution=approximate(B=9999)))
[1] 0.00330033

library(perm)                    # for permTS()
permTS(DV ~ IV, alternative="greater", method="exact.mc", 
       control=permControl(nmc=10^4-1))$p.value
[1] 0.003

library(exactRankTests)          # for perm.test()
perm.test(DV ~ IV, paired=FALSE, alternative="greater", exact=TRUE)$p.value
[1] 0.003171822


To check the exact p-value with a manual calculation of all permutations, I'll restrict the data to the first 9 values.

x1 <- x1[1:9]
y1 <- y1[1:9]
DV <- c(x1, y1)
IV <- factor(rep(c("A", "B"), c(length(x1), length(y1))))
pvalue(oneway_test(DV ~ IV, alternative="greater", distribution="exact"))
[1] 0.0945907

permTS(DV ~ IV, alternative="greater", exact=TRUE)$p.value
[1] 0.0945907

# perm.test() gives different result due to rounding of input values
perm.test(DV ~ IV, paired=FALSE, alternative="greater", exact=TRUE)$p.value
[1] 0.1029412

# manual exact permutation test
idx  <- seq(along=DV)                 # indices to permute
idxA <- combn(idx, length(x1))        # all possibilities for different groups

# function to calculate difference in group means given index vector for group A
getDiffM <- function(x) { mean(DV[x]) - mean(DV[!(idx %in% x)]) }
resDM    <- apply(idxA, 2, getDiffM)  # difference in means for all permutations
diffM    <- mean(x1) - mean(y1)       # empirical differencen in group means

# p-value: proportion of group means at least as extreme as observed one
(pVal <- sum(resDM >= diffM) / length(resDM))
[1] 0.0945907


coin and exactRankTests are both from the same author, but coin seems to be more general and extensive - also in terms of documentation. exactRankTests is not actively developed anymore. I'd therefore choose coin (also because of informative functions like support()), unless you don't like to deal with S4 objects.

EDIT: for two dependent variables, the syntax is

id <- factor(rep(1:length(x1), 2))    # factor for participant
pvalue(oneway_test(DV ~ IV | id, alternative="greater",
                   distribution=approximate(B=9999)))
[1] 0.00810081

