With the cost of Next generation sequencing dropping ( you could probably do the whole parasite genome for $1500 max) I wouldn't waste too much time finding good primers. Isolate genomic DNA, send to a NGS core facility somewhere and wait 1 month for the data. Then you don't have to worry about trying to find good primer sequences.
I know this might seem a bit obvious-however, I would suggest starting with a few large parasitic primers-(maybe as many as 8-10) from similar taxa. My experience is not in parasites and I have limited information about what your working on so I would not be so bold as to suggest any particular ones-although I am sure you know of plenty of them anyway.
Once you get something that works you can actually start the sequencing process and refine it more towards your research goals. It will be vast quantity of data for you to shift through, however, it is probably the fastest method I can recommend, and similar species will have the highest chance of working for you.
I say look for the primers used in related parasites species if PCR works you can further modified the sequences of primers. that is you will do primer fishing
I believe you can start by using taxonomy. Just find the most related organism to your research species and use that to find potential sequencing primers through online databases.
Use primers for conserved genes from species with high relevance. Then sent the pcr product for sequencing and compare (blast) the results to identify the gene. This has many chances to work.
With the cost of Next generation sequencing dropping ( you could probably do the whole parasite genome for $1500 max) I wouldn't waste too much time finding good primers. Isolate genomic DNA, send to a NGS core facility somewhere and wait 1 month for the data. Then you don't have to worry about trying to find good primer sequences.
Like Colin and Mustapha pointed out, if you have the money you can go for whole genome sequencing. It will save you a lot of resources and precious time. Considering that time is money, having to spend $2000 for a whole genome sequencing in quite cheap.
If I do not have money (sequencing the genome is the best - I agree), I would study the nearest species (like others have suggested). I would first identify certain known 'genes/regions of interest' - if any, and start with conserved regions. If very less gene/sequence information is available, then random primers and/or 'primer-walking' would be the only option left. I would also not forget that, while it is OK to take up this approach for a preliminary insight, it might eventually be more expensive (to get meaningful information) than the whole genome sequencing. [smaller the parasite genome particularly cost lesser]. In all cases, isolating good quality of DNA from pure parasite-cells is the key.
You could buy random primers for PCR. However, you will need to identify the products. This could be done simply, create a cDNA library, then transfect the gene into a suitable species and hope that the proteins are expressible.