Is there a way to make the Beta distribution have support from 0 to 2, instead of 0 to 1?
Sure: define the CDF or PDF in terms of
- $C'(x,\alpha, \beta) = C(x/2, \alpha, \beta)$
- $P'(x,\alpha,\beta) = P(x/2,\alpha,\beta)/2$
where $C$ and $P$ are the original Beta CDF and PDF and $C'$ and $P'$ are the new ones (and $\alpha$ and $\beta$ are the two shape parameters).
Wikipedia describes a four-parameter beta distribution which includes both an arbitrary scale parameter (which would be 2 in your case) as well as a shift parameter (which would be 0 for you, since you want the left endpoint of the distribution to stay at zero rather than shifting).